On the Location of Roots of the Characteristic Polynomial of (p, q)-Distance Fibonacci Sequences

Abstract Let p, q, k and %$\ell %$ be positive integers. The %$(p,q,k,\ell )%$-Fibonacci sequence %$(F_{k,\ell ,p,q})_{n\ge 0}%$ is the four-parameter sequence defined by the following recurrence Fk,ℓ,p,q(n)=kFk,ℓ,p,q(n-p)+ℓFk,ℓ,p,q(n-q),%$\begin{aligned} F_{k,\ell ,p,q}(n)=kF_{k,\ell ,p,q}(n-p)+\el...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Marques, Diego [verfasserIn] Trojovský, Pavel

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Generalized Fibonacci sequence Linear recurrence sequence Characteristic polynomial Eneström–Kakeya theorem Descartes’ sign rule Rouché’s theorem.

Anmerkung:	© Sociedade Brasileira de Matemática 2022

Übergeordnetes Werk:	Enthalten in: Bulletin of the Brazilian Mathematical Society - Heidelberg [u.a.] : Springer, 1970, 53(2022), 4 vom: 22. Juni, Seite 1231-1244
Übergeordnetes Werk:	volume:53 ; year:2022 ; number:4 ; day:22 ; month:06 ; pages:1231-1244

Links:	Volltext

DOI / URN:	10.1007/s00574-022-00301-z

Katalog-ID:	SPR048479950

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245	1	0	\|a On the Location of Roots of the Characteristic Polynomial of (p, q)-Distance Fibonacci Sequences
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520			\|a Abstract Let p, q, k and %$\ell %$ be positive integers. The %$(p,q,k,\ell )%$-Fibonacci sequence %$(F_{k,\ell ,p,q})_{n\ge 0}%$ is the four-parameter sequence defined by the following recurrence Fk,ℓ,p,q(n)=kFk,ℓ,p,q(n-p)+ℓFk,ℓ,p,q(n-q),%$\begin{aligned} F_{k,\ell ,p,q}(n)=kF_{k,\ell ,p,q}(n-p)+\ell F_{k,\ell ,p,q}(n-q), \end{aligned}%$with appropriate initial conditions. In this paper, we study the geometric, algebraic, and analytic aspects of the roots of the characteristic polynomial of this sequence, namely, %$f(x)=x^q-kx^{q-p}-\ell %$.
650		4	\|a Generalized Fibonacci sequence \|7 (dpeaa)DE-He213
650		4	\|a Linear recurrence sequence \|7 (dpeaa)DE-He213
650		4	\|a Characteristic polynomial \|7 (dpeaa)DE-He213
650		4	\|a Eneström–Kakeya theorem \|7 (dpeaa)DE-He213
650		4	\|a Descartes’ sign rule \|7 (dpeaa)DE-He213
650		4	\|a Rouché’s theorem. \|7 (dpeaa)DE-He213
700	1		\|a Trojovský, Pavel \|4 aut
773	0	8	\|i Enthalten in \|t Bulletin of the Brazilian Mathematical Society \|d Heidelberg [u.a.] : Springer, 1970 \|g 53(2022), 4 vom: 22. Juni, Seite 1231-1244 \|w (DE-627)356885062 \|w (DE-600)2093151-7 \|x 1678-7714 \|7 nnns
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856	4	0	\|u https://dx.doi.org/10.1007/s00574-022-00301-z \|z lizenzpflichtig \|3 Volltext
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912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
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publishDate	2022
allfields	10.1007/s00574-022-00301-z doi (DE-627)SPR048479950 (SPR)s00574-022-00301-z-e DE-627 ger DE-627 rakwb eng Marques, Diego verfasserin aut On the Location of Roots of the Characteristic Polynomial of (p, q)-Distance Fibonacci Sequences 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedade Brasileira de Matemática 2022 Abstract Let p, q, k and %$\ell %$ be positive integers. The %$(p,q,k,\ell )%$-Fibonacci sequence %$(F_{k,\ell ,p,q})_{n\ge 0}%$ is the four-parameter sequence defined by the following recurrence Fk,ℓ,p,q(n)=kFk,ℓ,p,q(n-p)+ℓFk,ℓ,p,q(n-q),%$\begin{aligned} F_{k,\ell ,p,q}(n)=kF_{k,\ell ,p,q}(n-p)+\ell F_{k,\ell ,p,q}(n-q), \end{aligned}%$with appropriate initial conditions. In this paper, we study the geometric, algebraic, and analytic aspects of the roots of the characteristic polynomial of this sequence, namely, %$f(x)=x^q-kx^{q-p}-\ell %$. Generalized Fibonacci sequence (dpeaa)DE-He213 Linear recurrence sequence (dpeaa)DE-He213 Characteristic polynomial (dpeaa)DE-He213 Eneström–Kakeya theorem (dpeaa)DE-He213 Descartes’ sign rule (dpeaa)DE-He213 Rouché’s theorem. (dpeaa)DE-He213 Trojovský, Pavel aut Enthalten in Bulletin of the Brazilian Mathematical Society Heidelberg [u.a.] : Springer, 1970 53(2022), 4 vom: 22. Juni, Seite 1231-1244 (DE-627)356885062 (DE-600)2093151-7 1678-7714 nnns volume:53 year:2022 number:4 day:22 month:06 pages:1231-1244 https://dx.doi.org/10.1007/s00574-022-00301-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 53 2022 4 22 06 1231-1244
spelling	10.1007/s00574-022-00301-z doi (DE-627)SPR048479950 (SPR)s00574-022-00301-z-e DE-627 ger DE-627 rakwb eng Marques, Diego verfasserin aut On the Location of Roots of the Characteristic Polynomial of (p, q)-Distance Fibonacci Sequences 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedade Brasileira de Matemática 2022 Abstract Let p, q, k and %$\ell %$ be positive integers. The %$(p,q,k,\ell )%$-Fibonacci sequence %$(F_{k,\ell ,p,q})_{n\ge 0}%$ is the four-parameter sequence defined by the following recurrence Fk,ℓ,p,q(n)=kFk,ℓ,p,q(n-p)+ℓFk,ℓ,p,q(n-q),%$\begin{aligned} F_{k,\ell ,p,q}(n)=kF_{k,\ell ,p,q}(n-p)+\ell F_{k,\ell ,p,q}(n-q), \end{aligned}%$with appropriate initial conditions. In this paper, we study the geometric, algebraic, and analytic aspects of the roots of the characteristic polynomial of this sequence, namely, %$f(x)=x^q-kx^{q-p}-\ell %$. Generalized Fibonacci sequence (dpeaa)DE-He213 Linear recurrence sequence (dpeaa)DE-He213 Characteristic polynomial (dpeaa)DE-He213 Eneström–Kakeya theorem (dpeaa)DE-He213 Descartes’ sign rule (dpeaa)DE-He213 Rouché’s theorem. (dpeaa)DE-He213 Trojovský, Pavel aut Enthalten in Bulletin of the Brazilian Mathematical Society Heidelberg [u.a.] : Springer, 1970 53(2022), 4 vom: 22. Juni, Seite 1231-1244 (DE-627)356885062 (DE-600)2093151-7 1678-7714 nnns volume:53 year:2022 number:4 day:22 month:06 pages:1231-1244 https://dx.doi.org/10.1007/s00574-022-00301-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 53 2022 4 22 06 1231-1244
allfields_unstemmed	10.1007/s00574-022-00301-z doi (DE-627)SPR048479950 (SPR)s00574-022-00301-z-e DE-627 ger DE-627 rakwb eng Marques, Diego verfasserin aut On the Location of Roots of the Characteristic Polynomial of (p, q)-Distance Fibonacci Sequences 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedade Brasileira de Matemática 2022 Abstract Let p, q, k and %$\ell %$ be positive integers. The %$(p,q,k,\ell )%$-Fibonacci sequence %$(F_{k,\ell ,p,q})_{n\ge 0}%$ is the four-parameter sequence defined by the following recurrence Fk,ℓ,p,q(n)=kFk,ℓ,p,q(n-p)+ℓFk,ℓ,p,q(n-q),%$\begin{aligned} F_{k,\ell ,p,q}(n)=kF_{k,\ell ,p,q}(n-p)+\ell F_{k,\ell ,p,q}(n-q), \end{aligned}%$with appropriate initial conditions. In this paper, we study the geometric, algebraic, and analytic aspects of the roots of the characteristic polynomial of this sequence, namely, %$f(x)=x^q-kx^{q-p}-\ell %$. Generalized Fibonacci sequence (dpeaa)DE-He213 Linear recurrence sequence (dpeaa)DE-He213 Characteristic polynomial (dpeaa)DE-He213 Eneström–Kakeya theorem (dpeaa)DE-He213 Descartes’ sign rule (dpeaa)DE-He213 Rouché’s theorem. (dpeaa)DE-He213 Trojovský, Pavel aut Enthalten in Bulletin of the Brazilian Mathematical Society Heidelberg [u.a.] : Springer, 1970 53(2022), 4 vom: 22. Juni, Seite 1231-1244 (DE-627)356885062 (DE-600)2093151-7 1678-7714 nnns volume:53 year:2022 number:4 day:22 month:06 pages:1231-1244 https://dx.doi.org/10.1007/s00574-022-00301-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 53 2022 4 22 06 1231-1244
allfieldsGer	10.1007/s00574-022-00301-z doi (DE-627)SPR048479950 (SPR)s00574-022-00301-z-e DE-627 ger DE-627 rakwb eng Marques, Diego verfasserin aut On the Location of Roots of the Characteristic Polynomial of (p, q)-Distance Fibonacci Sequences 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedade Brasileira de Matemática 2022 Abstract Let p, q, k and %$\ell %$ be positive integers. The %$(p,q,k,\ell )%$-Fibonacci sequence %$(F_{k,\ell ,p,q})_{n\ge 0}%$ is the four-parameter sequence defined by the following recurrence Fk,ℓ,p,q(n)=kFk,ℓ,p,q(n-p)+ℓFk,ℓ,p,q(n-q),%$\begin{aligned} F_{k,\ell ,p,q}(n)=kF_{k,\ell ,p,q}(n-p)+\ell F_{k,\ell ,p,q}(n-q), \end{aligned}%$with appropriate initial conditions. In this paper, we study the geometric, algebraic, and analytic aspects of the roots of the characteristic polynomial of this sequence, namely, %$f(x)=x^q-kx^{q-p}-\ell %$. Generalized Fibonacci sequence (dpeaa)DE-He213 Linear recurrence sequence (dpeaa)DE-He213 Characteristic polynomial (dpeaa)DE-He213 Eneström–Kakeya theorem (dpeaa)DE-He213 Descartes’ sign rule (dpeaa)DE-He213 Rouché’s theorem. (dpeaa)DE-He213 Trojovský, Pavel aut Enthalten in Bulletin of the Brazilian Mathematical Society Heidelberg [u.a.] : Springer, 1970 53(2022), 4 vom: 22. Juni, Seite 1231-1244 (DE-627)356885062 (DE-600)2093151-7 1678-7714 nnns volume:53 year:2022 number:4 day:22 month:06 pages:1231-1244 https://dx.doi.org/10.1007/s00574-022-00301-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 53 2022 4 22 06 1231-1244
allfieldsSound	10.1007/s00574-022-00301-z doi (DE-627)SPR048479950 (SPR)s00574-022-00301-z-e DE-627 ger DE-627 rakwb eng Marques, Diego verfasserin aut On the Location of Roots of the Characteristic Polynomial of (p, q)-Distance Fibonacci Sequences 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedade Brasileira de Matemática 2022 Abstract Let p, q, k and %$\ell %$ be positive integers. The %$(p,q,k,\ell )%$-Fibonacci sequence %$(F_{k,\ell ,p,q})_{n\ge 0}%$ is the four-parameter sequence defined by the following recurrence Fk,ℓ,p,q(n)=kFk,ℓ,p,q(n-p)+ℓFk,ℓ,p,q(n-q),%$\begin{aligned} F_{k,\ell ,p,q}(n)=kF_{k,\ell ,p,q}(n-p)+\ell F_{k,\ell ,p,q}(n-q), \end{aligned}%$with appropriate initial conditions. In this paper, we study the geometric, algebraic, and analytic aspects of the roots of the characteristic polynomial of this sequence, namely, %$f(x)=x^q-kx^{q-p}-\ell %$. Generalized Fibonacci sequence (dpeaa)DE-He213 Linear recurrence sequence (dpeaa)DE-He213 Characteristic polynomial (dpeaa)DE-He213 Eneström–Kakeya theorem (dpeaa)DE-He213 Descartes’ sign rule (dpeaa)DE-He213 Rouché’s theorem. (dpeaa)DE-He213 Trojovský, Pavel aut Enthalten in Bulletin of the Brazilian Mathematical Society Heidelberg [u.a.] : Springer, 1970 53(2022), 4 vom: 22. Juni, Seite 1231-1244 (DE-627)356885062 (DE-600)2093151-7 1678-7714 nnns volume:53 year:2022 number:4 day:22 month:06 pages:1231-1244 https://dx.doi.org/10.1007/s00574-022-00301-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 53 2022 4 22 06 1231-1244
language	English
source	Enthalten in Bulletin of the Brazilian Mathematical Society 53(2022), 4 vom: 22. Juni, Seite 1231-1244 volume:53 year:2022 number:4 day:22 month:06 pages:1231-1244
sourceStr	Enthalten in Bulletin of the Brazilian Mathematical Society 53(2022), 4 vom: 22. Juni, Seite 1231-1244 volume:53 year:2022 number:4 day:22 month:06 pages:1231-1244
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Generalized Fibonacci sequence Linear recurrence sequence Characteristic polynomial Eneström–Kakeya theorem Descartes’ sign rule Rouché’s theorem.
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container_title	Bulletin of the Brazilian Mathematical Society
authorswithroles_txt_mv	Marques, Diego @@aut@@ Trojovský, Pavel @@aut@@
publishDateDaySort_date	2022-06-22T00:00:00Z
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author	Marques, Diego
spellingShingle	Marques, Diego misc Generalized Fibonacci sequence misc Linear recurrence sequence misc Characteristic polynomial misc Eneström–Kakeya theorem misc Descartes’ sign rule misc Rouché’s theorem. On the Location of Roots of the Characteristic Polynomial of (p, q)-Distance Fibonacci Sequences
authorStr	Marques, Diego
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topic_title	On the Location of Roots of the Characteristic Polynomial of (p, q)-Distance Fibonacci Sequences Generalized Fibonacci sequence (dpeaa)DE-He213 Linear recurrence sequence (dpeaa)DE-He213 Characteristic polynomial (dpeaa)DE-He213 Eneström–Kakeya theorem (dpeaa)DE-He213 Descartes’ sign rule (dpeaa)DE-He213 Rouché’s theorem. (dpeaa)DE-He213
topic	misc Generalized Fibonacci sequence misc Linear recurrence sequence misc Characteristic polynomial misc Eneström–Kakeya theorem misc Descartes’ sign rule misc Rouché’s theorem.
topic_unstemmed	misc Generalized Fibonacci sequence misc Linear recurrence sequence misc Characteristic polynomial misc Eneström–Kakeya theorem misc Descartes’ sign rule misc Rouché’s theorem.
topic_browse	misc Generalized Fibonacci sequence misc Linear recurrence sequence misc Characteristic polynomial misc Eneström–Kakeya theorem misc Descartes’ sign rule misc Rouché’s theorem.
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title	On the Location of Roots of the Characteristic Polynomial of (p, q)-Distance Fibonacci Sequences
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title_full	On the Location of Roots of the Characteristic Polynomial of (p, q)-Distance Fibonacci Sequences
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doi_str_mv	10.1007/s00574-022-00301-z
title_sort	on the location of roots of the characteristic polynomial of (p, q)-distance fibonacci sequences
title_auth	On the Location of Roots of the Characteristic Polynomial of (p, q)-Distance Fibonacci Sequences
abstract	Abstract Let p, q, k and %$\ell %$ be positive integers. The %$(p,q,k,\ell )%$-Fibonacci sequence %$(F_{k,\ell ,p,q})_{n\ge 0}%$ is the four-parameter sequence defined by the following recurrence Fk,ℓ,p,q(n)=kFk,ℓ,p,q(n-p)+ℓFk,ℓ,p,q(n-q),%$\begin{aligned} F_{k,\ell ,p,q}(n)=kF_{k,\ell ,p,q}(n-p)+\ell F_{k,\ell ,p,q}(n-q), \end{aligned}%$with appropriate initial conditions. In this paper, we study the geometric, algebraic, and analytic aspects of the roots of the characteristic polynomial of this sequence, namely, %$f(x)=x^q-kx^{q-p}-\ell %$. © Sociedade Brasileira de Matemática 2022
abstractGer	Abstract Let p, q, k and %$\ell %$ be positive integers. The %$(p,q,k,\ell )%$-Fibonacci sequence %$(F_{k,\ell ,p,q})_{n\ge 0}%$ is the four-parameter sequence defined by the following recurrence Fk,ℓ,p,q(n)=kFk,ℓ,p,q(n-p)+ℓFk,ℓ,p,q(n-q),%$\begin{aligned} F_{k,\ell ,p,q}(n)=kF_{k,\ell ,p,q}(n-p)+\ell F_{k,\ell ,p,q}(n-q), \end{aligned}%$with appropriate initial conditions. In this paper, we study the geometric, algebraic, and analytic aspects of the roots of the characteristic polynomial of this sequence, namely, %$f(x)=x^q-kx^{q-p}-\ell %$. © Sociedade Brasileira de Matemática 2022
abstract_unstemmed	Abstract Let p, q, k and %$\ell %$ be positive integers. The %$(p,q,k,\ell )%$-Fibonacci sequence %$(F_{k,\ell ,p,q})_{n\ge 0}%$ is the four-parameter sequence defined by the following recurrence Fk,ℓ,p,q(n)=kFk,ℓ,p,q(n-p)+ℓFk,ℓ,p,q(n-q),%$\begin{aligned} F_{k,\ell ,p,q}(n)=kF_{k,\ell ,p,q}(n-p)+\ell F_{k,\ell ,p,q}(n-q), \end{aligned}%$with appropriate initial conditions. In this paper, we study the geometric, algebraic, and analytic aspects of the roots of the characteristic polynomial of this sequence, namely, %$f(x)=x^q-kx^{q-p}-\ell %$. © Sociedade Brasileira de Matemática 2022
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container_issue	4
title_short	On the Location of Roots of the Characteristic Polynomial of (p, q)-Distance Fibonacci Sequences
url	https://dx.doi.org/10.1007/s00574-022-00301-z
remote_bool	true
author2	Trojovský, Pavel
author2Str	Trojovský, Pavel
ppnlink	356885062
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doi_str	10.1007/s00574-022-00301-z
up_date	2024-07-03T19:29:15.873Z
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On the Location of Roots of the Characteristic Polynomial of (p, q)-Distance Fibonacci Sequences

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