Determinantal Formulas for SEM Expansions of Schubert Polynomials

Abstract We show that for any permutation w that avoids a certain set of 13 patterns of length 5 and 6, the Schubert polynomial %${\mathfrak {S}}_w%$ can be expressed as the determinant of a matrix of elementary symmetric polynomials in a manner similar to the Jacobi–Trudi identity. For such w, this...
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Autor*in:	Hatam, Hassan [verfasserIn] Johnson, Joseph [verfasserIn] Liu, Ricky Ini [verfasserIn] Macaulay, Maria [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Anmerkung:	© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021

Übergeordnetes Werk:	Enthalten in: Annals of combinatorics - [Cham (ZG)] : [Springer International Publishing AG], 1997, 25(2021), 4 vom: 23. Okt., Seite 1049-1074
Übergeordnetes Werk:	volume:25 ; year:2021 ; number:4 ; day:23 ; month:10 ; pages:1049-1074

Links:	Volltext

DOI / URN:	10.1007/s00026-021-00558-z

Katalog-ID:	SPR045717621

Internformat


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520			\|a Abstract We show that for any permutation w that avoids a certain set of 13 patterns of length 5 and 6, the Schubert polynomial %${\mathfrak {S}}_w%$ can be expressed as the determinant of a matrix of elementary symmetric polynomials in a manner similar to the Jacobi–Trudi identity. For such w, this determinantal formula is equivalent to a (signed) subtraction-free expansion of %$\mathfrak S_w%$ in the basis of standard elementary monomials.
700	1		\|a Johnson, Joseph \|e verfasserin \|4 aut
700	1		\|a Liu, Ricky Ini \|e verfasserin \|4 aut
700	1		\|a Macaulay, Maria \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Annals of combinatorics \|d [Cham (ZG)] : [Springer International Publishing AG], 1997 \|g 25(2021), 4 vom: 23. Okt., Seite 1049-1074 \|w (DE-627)27159618X \|w (DE-600)1480599-6 \|x 0219-3094 \|7 nnns
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856	4	0	\|u https://dx.doi.org/10.1007/s00026-021-00558-z \|z lizenzpflichtig \|3 Volltext
912			\|a GBV_USEFLAG_A
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912			\|a GBV_ILN_11
912			\|a GBV_ILN_20
912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
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_267
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
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
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Indexfelder

author_variant	h h hh j j jj r i l ri ril m m mm
matchkey_str	article:02193094:2021----::eemnnafruafreepninosh
hierarchy_sort_str	2021
bklnumber	31.00
publishDate	2021
allfields	10.1007/s00026-021-00558-z doi (DE-627)SPR045717621 (SPR)s00026-021-00558-z-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Hatam, Hassan verfasserin aut Determinantal Formulas for SEM Expansions of Schubert Polynomials 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract We show that for any permutation w that avoids a certain set of 13 patterns of length 5 and 6, the Schubert polynomial %${\mathfrak {S}}_w%$ can be expressed as the determinant of a matrix of elementary symmetric polynomials in a manner similar to the Jacobi–Trudi identity. For such w, this determinantal formula is equivalent to a (signed) subtraction-free expansion of %$\mathfrak S_w%$ in the basis of standard elementary monomials. Johnson, Joseph verfasserin aut Liu, Ricky Ini verfasserin aut Macaulay, Maria verfasserin aut Enthalten in Annals of combinatorics [Cham (ZG)] : [Springer International Publishing AG], 1997 25(2021), 4 vom: 23. Okt., Seite 1049-1074 (DE-627)27159618X (DE-600)1480599-6 0219-3094 nnns volume:25 year:2021 number:4 day:23 month:10 pages:1049-1074 https://dx.doi.org/10.1007/s00026-021-00558-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_267 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 31.00 ASE AR 25 2021 4 23 10 1049-1074
spelling	10.1007/s00026-021-00558-z doi (DE-627)SPR045717621 (SPR)s00026-021-00558-z-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Hatam, Hassan verfasserin aut Determinantal Formulas for SEM Expansions of Schubert Polynomials 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract We show that for any permutation w that avoids a certain set of 13 patterns of length 5 and 6, the Schubert polynomial %${\mathfrak {S}}_w%$ can be expressed as the determinant of a matrix of elementary symmetric polynomials in a manner similar to the Jacobi–Trudi identity. For such w, this determinantal formula is equivalent to a (signed) subtraction-free expansion of %$\mathfrak S_w%$ in the basis of standard elementary monomials. Johnson, Joseph verfasserin aut Liu, Ricky Ini verfasserin aut Macaulay, Maria verfasserin aut Enthalten in Annals of combinatorics [Cham (ZG)] : [Springer International Publishing AG], 1997 25(2021), 4 vom: 23. Okt., Seite 1049-1074 (DE-627)27159618X (DE-600)1480599-6 0219-3094 nnns volume:25 year:2021 number:4 day:23 month:10 pages:1049-1074 https://dx.doi.org/10.1007/s00026-021-00558-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_267 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 31.00 ASE AR 25 2021 4 23 10 1049-1074
allfields_unstemmed	10.1007/s00026-021-00558-z doi (DE-627)SPR045717621 (SPR)s00026-021-00558-z-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Hatam, Hassan verfasserin aut Determinantal Formulas for SEM Expansions of Schubert Polynomials 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract We show that for any permutation w that avoids a certain set of 13 patterns of length 5 and 6, the Schubert polynomial %${\mathfrak {S}}_w%$ can be expressed as the determinant of a matrix of elementary symmetric polynomials in a manner similar to the Jacobi–Trudi identity. For such w, this determinantal formula is equivalent to a (signed) subtraction-free expansion of %$\mathfrak S_w%$ in the basis of standard elementary monomials. Johnson, Joseph verfasserin aut Liu, Ricky Ini verfasserin aut Macaulay, Maria verfasserin aut Enthalten in Annals of combinatorics [Cham (ZG)] : [Springer International Publishing AG], 1997 25(2021), 4 vom: 23. Okt., Seite 1049-1074 (DE-627)27159618X (DE-600)1480599-6 0219-3094 nnns volume:25 year:2021 number:4 day:23 month:10 pages:1049-1074 https://dx.doi.org/10.1007/s00026-021-00558-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_267 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 31.00 ASE AR 25 2021 4 23 10 1049-1074
allfieldsGer	10.1007/s00026-021-00558-z doi (DE-627)SPR045717621 (SPR)s00026-021-00558-z-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Hatam, Hassan verfasserin aut Determinantal Formulas for SEM Expansions of Schubert Polynomials 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract We show that for any permutation w that avoids a certain set of 13 patterns of length 5 and 6, the Schubert polynomial %${\mathfrak {S}}_w%$ can be expressed as the determinant of a matrix of elementary symmetric polynomials in a manner similar to the Jacobi–Trudi identity. For such w, this determinantal formula is equivalent to a (signed) subtraction-free expansion of %$\mathfrak S_w%$ in the basis of standard elementary monomials. Johnson, Joseph verfasserin aut Liu, Ricky Ini verfasserin aut Macaulay, Maria verfasserin aut Enthalten in Annals of combinatorics [Cham (ZG)] : [Springer International Publishing AG], 1997 25(2021), 4 vom: 23. Okt., Seite 1049-1074 (DE-627)27159618X (DE-600)1480599-6 0219-3094 nnns volume:25 year:2021 number:4 day:23 month:10 pages:1049-1074 https://dx.doi.org/10.1007/s00026-021-00558-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_267 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 31.00 ASE AR 25 2021 4 23 10 1049-1074
allfieldsSound	10.1007/s00026-021-00558-z doi (DE-627)SPR045717621 (SPR)s00026-021-00558-z-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Hatam, Hassan verfasserin aut Determinantal Formulas for SEM Expansions of Schubert Polynomials 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021 Abstract We show that for any permutation w that avoids a certain set of 13 patterns of length 5 and 6, the Schubert polynomial %${\mathfrak {S}}_w%$ can be expressed as the determinant of a matrix of elementary symmetric polynomials in a manner similar to the Jacobi–Trudi identity. For such w, this determinantal formula is equivalent to a (signed) subtraction-free expansion of %$\mathfrak S_w%$ in the basis of standard elementary monomials. Johnson, Joseph verfasserin aut Liu, Ricky Ini verfasserin aut Macaulay, Maria verfasserin aut Enthalten in Annals of combinatorics [Cham (ZG)] : [Springer International Publishing AG], 1997 25(2021), 4 vom: 23. Okt., Seite 1049-1074 (DE-627)27159618X (DE-600)1480599-6 0219-3094 nnns volume:25 year:2021 number:4 day:23 month:10 pages:1049-1074 https://dx.doi.org/10.1007/s00026-021-00558-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_267 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 31.00 ASE AR 25 2021 4 23 10 1049-1074
language	English
source	Enthalten in Annals of combinatorics 25(2021), 4 vom: 23. Okt., Seite 1049-1074 volume:25 year:2021 number:4 day:23 month:10 pages:1049-1074
sourceStr	Enthalten in Annals of combinatorics 25(2021), 4 vom: 23. Okt., Seite 1049-1074 volume:25 year:2021 number:4 day:23 month:10 pages:1049-1074
format_phy_str_mv	Article
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isfreeaccess_bool	false
container_title	Annals of combinatorics
authorswithroles_txt_mv	Hatam, Hassan @@aut@@ Johnson, Joseph @@aut@@ Liu, Ricky Ini @@aut@@ Macaulay, Maria @@aut@@
publishDateDaySort_date	2021-10-23T00:00:00Z
hierarchy_top_id	27159618X
dewey-sort	3510
id	SPR045717621
language_de	englisch
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author	Hatam, Hassan
spellingShingle	Hatam, Hassan ddc 510 bkl 31.00 Determinantal Formulas for SEM Expansions of Schubert Polynomials
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topic_title	510 ASE 31.00 bkl Determinantal Formulas for SEM Expansions of Schubert Polynomials
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title	Determinantal Formulas for SEM Expansions of Schubert Polynomials
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title_full	Determinantal Formulas for SEM Expansions of Schubert Polynomials
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author_browse	Hatam, Hassan Johnson, Joseph Liu, Ricky Ini Macaulay, Maria
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title_sort	determinantal formulas for sem expansions of schubert polynomials
title_auth	Determinantal Formulas for SEM Expansions of Schubert Polynomials
abstract	Abstract We show that for any permutation w that avoids a certain set of 13 patterns of length 5 and 6, the Schubert polynomial %${\mathfrak {S}}_w%$ can be expressed as the determinant of a matrix of elementary symmetric polynomials in a manner similar to the Jacobi–Trudi identity. For such w, this determinantal formula is equivalent to a (signed) subtraction-free expansion of %$\mathfrak S_w%$ in the basis of standard elementary monomials. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021
abstractGer	Abstract We show that for any permutation w that avoids a certain set of 13 patterns of length 5 and 6, the Schubert polynomial %${\mathfrak {S}}_w%$ can be expressed as the determinant of a matrix of elementary symmetric polynomials in a manner similar to the Jacobi–Trudi identity. For such w, this determinantal formula is equivalent to a (signed) subtraction-free expansion of %$\mathfrak S_w%$ in the basis of standard elementary monomials. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021
abstract_unstemmed	Abstract We show that for any permutation w that avoids a certain set of 13 patterns of length 5 and 6, the Schubert polynomial %${\mathfrak {S}}_w%$ can be expressed as the determinant of a matrix of elementary symmetric polynomials in a manner similar to the Jacobi–Trudi identity. For such w, this determinantal formula is equivalent to a (signed) subtraction-free expansion of %$\mathfrak S_w%$ in the basis of standard elementary monomials. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021
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title_short	Determinantal Formulas for SEM Expansions of Schubert Polynomials
url	https://dx.doi.org/10.1007/s00026-021-00558-z
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author2	Johnson, Joseph Liu, Ricky Ini Macaulay, Maria
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up_date	2024-07-03T17:50:50.013Z
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For such w, this determinantal formula is equivalent to a (signed) subtraction-free expansion of %$\mathfrak S_w%$ in the basis of standard elementary monomials.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Johnson, Joseph</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Liu, Ricky Ini</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Macaulay, Maria</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Annals of combinatorics</subfield><subfield code="d">[Cham (ZG)] : [Springer International Publishing AG], 1997</subfield><subfield code="g">25(2021), 4 vom: 23. 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