The minimum size of a linear set

In this paper, we first determine the minimum possible size of an F q -linear set of rank k in...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	De Beule, Jan [verfasserIn] Van de Voorde, Geertrui [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Linear set Linearised polynomial Directions determined by a point set

Übergeordnetes Werk:	Enthalten in: Journal of combinatorial theory / A - Amsterdam [u.a.] : Elsevier, 1971, 164, Seite 109-124
Übergeordnetes Werk:	volume:164 ; pages:109-124

DOI / URN:	10.1016/j.jcta.2018.12.008

Katalog-ID:	ELV001549111

Internformat


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520			\|a In this paper, we first determine the minimum possible size of an F q -linear set of rank k in PG ( 1 , q n ) . We obtain this result by relating it to the number of directions determined by a linearized polynomial whose domain is restricted to a subspace. We then use this result to find a lower bound on the number of points in an F q -linear set of rank k in PG ( 2 , q n ) . In the case k = n , this confirms a conjecture by Sziklai in .
650		4	\|a Linear set
650		4	\|a Linearised polynomial
650		4	\|a Directions determined by a point set
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912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
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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_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2011
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912			\|a GBV_ILN_2015
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912			\|a GBV_ILN_2021
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912			\|a GBV_ILN_2048
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912			\|a GBV_ILN_2050
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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_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_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
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912			\|a GBV_ILN_4393
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936	b	k	\|a 31.12 \|j Kombinatorik \|j Graphentheorie
951			\|a AR
952			\|d 164 \|h 109-124

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allfields	10.1016/j.jcta.2018.12.008 doi (DE-627)ELV001549111 (ELSEVIER)S0097-3165(19)30001-9 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl De Beule, Jan verfasserin (orcid)0000-0001-5333-5224 aut The minimum size of a linear set 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we first determine the minimum possible size of an F q -linear set of rank k in PG ( 1 , q n ) . We obtain this result by relating it to the number of directions determined by a linearized polynomial whose domain is restricted to a subspace. We then use this result to find a lower bound on the number of points in an F q -linear set of rank k in PG ( 2 , q n ) . In the case k = n , this confirms a conjecture by Sziklai in . Linear set Linearised polynomial Directions determined by a point set Van de Voorde, Geertrui verfasserin (orcid)0000-0002-4957-6911 aut Enthalten in Journal of combinatorial theory / A Amsterdam [u.a.] : Elsevier, 1971 164, Seite 109-124 Online-Ressource (DE-627)266892361 (DE-600)1469152-8 (DE-576)104193808 nnns volume:164 pages:109-124 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie AR 164 109-124
spelling	10.1016/j.jcta.2018.12.008 doi (DE-627)ELV001549111 (ELSEVIER)S0097-3165(19)30001-9 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl De Beule, Jan verfasserin (orcid)0000-0001-5333-5224 aut The minimum size of a linear set 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we first determine the minimum possible size of an F q -linear set of rank k in PG ( 1 , q n ) . We obtain this result by relating it to the number of directions determined by a linearized polynomial whose domain is restricted to a subspace. We then use this result to find a lower bound on the number of points in an F q -linear set of rank k in PG ( 2 , q n ) . In the case k = n , this confirms a conjecture by Sziklai in . Linear set Linearised polynomial Directions determined by a point set Van de Voorde, Geertrui verfasserin (orcid)0000-0002-4957-6911 aut Enthalten in Journal of combinatorial theory / A Amsterdam [u.a.] : Elsevier, 1971 164, Seite 109-124 Online-Ressource (DE-627)266892361 (DE-600)1469152-8 (DE-576)104193808 nnns volume:164 pages:109-124 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie AR 164 109-124
allfields_unstemmed	10.1016/j.jcta.2018.12.008 doi (DE-627)ELV001549111 (ELSEVIER)S0097-3165(19)30001-9 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl De Beule, Jan verfasserin (orcid)0000-0001-5333-5224 aut The minimum size of a linear set 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we first determine the minimum possible size of an F q -linear set of rank k in PG ( 1 , q n ) . We obtain this result by relating it to the number of directions determined by a linearized polynomial whose domain is restricted to a subspace. We then use this result to find a lower bound on the number of points in an F q -linear set of rank k in PG ( 2 , q n ) . In the case k = n , this confirms a conjecture by Sziklai in . Linear set Linearised polynomial Directions determined by a point set Van de Voorde, Geertrui verfasserin (orcid)0000-0002-4957-6911 aut Enthalten in Journal of combinatorial theory / A Amsterdam [u.a.] : Elsevier, 1971 164, Seite 109-124 Online-Ressource (DE-627)266892361 (DE-600)1469152-8 (DE-576)104193808 nnns volume:164 pages:109-124 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie AR 164 109-124
allfieldsGer	10.1016/j.jcta.2018.12.008 doi (DE-627)ELV001549111 (ELSEVIER)S0097-3165(19)30001-9 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl De Beule, Jan verfasserin (orcid)0000-0001-5333-5224 aut The minimum size of a linear set 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we first determine the minimum possible size of an F q -linear set of rank k in PG ( 1 , q n ) . We obtain this result by relating it to the number of directions determined by a linearized polynomial whose domain is restricted to a subspace. We then use this result to find a lower bound on the number of points in an F q -linear set of rank k in PG ( 2 , q n ) . In the case k = n , this confirms a conjecture by Sziklai in . Linear set Linearised polynomial Directions determined by a point set Van de Voorde, Geertrui verfasserin (orcid)0000-0002-4957-6911 aut Enthalten in Journal of combinatorial theory / A Amsterdam [u.a.] : Elsevier, 1971 164, Seite 109-124 Online-Ressource (DE-627)266892361 (DE-600)1469152-8 (DE-576)104193808 nnns volume:164 pages:109-124 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie AR 164 109-124
allfieldsSound	10.1016/j.jcta.2018.12.008 doi (DE-627)ELV001549111 (ELSEVIER)S0097-3165(19)30001-9 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl De Beule, Jan verfasserin (orcid)0000-0001-5333-5224 aut The minimum size of a linear set 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we first determine the minimum possible size of an F q -linear set of rank k in PG ( 1 , q n ) . We obtain this result by relating it to the number of directions determined by a linearized polynomial whose domain is restricted to a subspace. We then use this result to find a lower bound on the number of points in an F q -linear set of rank k in PG ( 2 , q n ) . In the case k = n , this confirms a conjecture by Sziklai in . Linear set Linearised polynomial Directions determined by a point set Van de Voorde, Geertrui verfasserin (orcid)0000-0002-4957-6911 aut Enthalten in Journal of combinatorial theory / A Amsterdam [u.a.] : Elsevier, 1971 164, Seite 109-124 Online-Ressource (DE-627)266892361 (DE-600)1469152-8 (DE-576)104193808 nnns volume:164 pages:109-124 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie AR 164 109-124
language	English
source	Enthalten in Journal of combinatorial theory / A 164, Seite 109-124 volume:164 pages:109-124
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title_full	The minimum size of a linear set
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title_sort	the minimum size of a linear set
title_auth	The minimum size of a linear set
abstract	In this paper, we first determine the minimum possible size of an F q -linear set of rank k in PG ( 1 , q n ) . We obtain this result by relating it to the number of directions determined by a linearized polynomial whose domain is restricted to a subspace. We then use this result to find a lower bound on the number of points in an F q -linear set of rank k in PG ( 2 , q n ) . In the case k = n , this confirms a conjecture by Sziklai in .
abstractGer	In this paper, we first determine the minimum possible size of an F q -linear set of rank k in PG ( 1 , q n ) . We obtain this result by relating it to the number of directions determined by a linearized polynomial whose domain is restricted to a subspace. We then use this result to find a lower bound on the number of points in an F q -linear set of rank k in PG ( 2 , q n ) . In the case k = n , this confirms a conjecture by Sziklai in .
abstract_unstemmed	In this paper, we first determine the minimum possible size of an F q -linear set of rank k in PG ( 1 , q n ) . We obtain this result by relating it to the number of directions determined by a linearized polynomial whose domain is restricted to a subspace. We then use this result to find a lower bound on the number of points in an F q -linear set of rank k in PG ( 2 , q n ) . In the case k = n , this confirms a conjecture by Sziklai in .
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title_short	The minimum size of a linear set
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We obtain this result by relating it to the number of directions determined by a linearized polynomial whose domain is restricted to a subspace. We then use this result to find a lower bound on the number of points in an F q -linear set of rank k in PG ( 2 , q n ) . 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