Hilbert series of simple thin polyominoes

Abstract Let %$\mathcal {P}%$ be a simple thin polyomino, namely a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced Hilbert–Poincaré series %$h(t)/(1-t)^d%$ of %$K[\mathcal {P}]%$ by proving that h(t) is the rook polynomia...
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Autor*in:	Rinaldo, Giancarlo [verfasserIn] Romeo, Francesco

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Simple polyominoes Hilbert–Poincaré series Rook polynomial Gorenstein algebras

Anmerkung:	© The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021

Übergeordnetes Werk:	Enthalten in: Journal of algebraic combinatorics - Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992, 54(2021), 2 vom: 05. Feb., Seite 607-624
Übergeordnetes Werk:	volume:54 ; year:2021 ; number:2 ; day:05 ; month:02 ; pages:607-624

Links:	Volltext

DOI / URN:	10.1007/s10801-021-01017-x

Katalog-ID:	SPR045246114

Internformat


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520			\|a Abstract Let %$\mathcal {P}%$ be a simple thin polyomino, namely a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced Hilbert–Poincaré series %$h(t)/(1-t)^d%$ of %$K[\mathcal {P}]%$ by proving that h(t) is the rook polynomial of %$\mathcal {P}%$. As an application, we characterize the Gorenstein simple thin polyominoes.
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650		4	\|a Hilbert–Poincaré series \|7 (dpeaa)DE-He213
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650		4	\|a Gorenstein algebras \|7 (dpeaa)DE-He213
700	1		\|a Romeo, Francesco \|4 aut
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912			\|a GBV_ILN_281
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912			\|a GBV_ILN_293
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matchkey_str	article:15729192:2021----::ibrsreosmltip
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publishDate	2021
allfields	10.1007/s10801-021-01017-x doi (DE-627)SPR045246114 (SPR)s10801-021-01017-x-e DE-627 ger DE-627 rakwb eng Rinaldo, Giancarlo verfasserin (orcid)0000-0003-3644-1142 aut Hilbert series of simple thin polyominoes 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021 Abstract Let %$\mathcal {P}%$ be a simple thin polyomino, namely a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced Hilbert–Poincaré series %$h(t)/(1-t)^d%$ of %$K[\mathcal {P}]%$ by proving that h(t) is the rook polynomial of %$\mathcal {P}%$. As an application, we characterize the Gorenstein simple thin polyominoes. Simple polyominoes (dpeaa)DE-He213 Hilbert–Poincaré series (dpeaa)DE-He213 Rook polynomial (dpeaa)DE-He213 Gorenstein algebras (dpeaa)DE-He213 Romeo, Francesco aut Enthalten in Journal of algebraic combinatorics Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992 54(2021), 2 vom: 05. Feb., Seite 607-624 (DE-627)271180722 (DE-600)1479499-8 1572-9192 nnns volume:54 year:2021 number:2 day:05 month:02 pages:607-624 https://dx.doi.org/10.1007/s10801-021-01017-x 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_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_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 54 2021 2 05 02 607-624
spelling	10.1007/s10801-021-01017-x doi (DE-627)SPR045246114 (SPR)s10801-021-01017-x-e DE-627 ger DE-627 rakwb eng Rinaldo, Giancarlo verfasserin (orcid)0000-0003-3644-1142 aut Hilbert series of simple thin polyominoes 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021 Abstract Let %$\mathcal {P}%$ be a simple thin polyomino, namely a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced Hilbert–Poincaré series %$h(t)/(1-t)^d%$ of %$K[\mathcal {P}]%$ by proving that h(t) is the rook polynomial of %$\mathcal {P}%$. As an application, we characterize the Gorenstein simple thin polyominoes. Simple polyominoes (dpeaa)DE-He213 Hilbert–Poincaré series (dpeaa)DE-He213 Rook polynomial (dpeaa)DE-He213 Gorenstein algebras (dpeaa)DE-He213 Romeo, Francesco aut Enthalten in Journal of algebraic combinatorics Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992 54(2021), 2 vom: 05. Feb., Seite 607-624 (DE-627)271180722 (DE-600)1479499-8 1572-9192 nnns volume:54 year:2021 number:2 day:05 month:02 pages:607-624 https://dx.doi.org/10.1007/s10801-021-01017-x 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_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_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 54 2021 2 05 02 607-624
allfields_unstemmed	10.1007/s10801-021-01017-x doi (DE-627)SPR045246114 (SPR)s10801-021-01017-x-e DE-627 ger DE-627 rakwb eng Rinaldo, Giancarlo verfasserin (orcid)0000-0003-3644-1142 aut Hilbert series of simple thin polyominoes 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021 Abstract Let %$\mathcal {P}%$ be a simple thin polyomino, namely a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced Hilbert–Poincaré series %$h(t)/(1-t)^d%$ of %$K[\mathcal {P}]%$ by proving that h(t) is the rook polynomial of %$\mathcal {P}%$. As an application, we characterize the Gorenstein simple thin polyominoes. Simple polyominoes (dpeaa)DE-He213 Hilbert–Poincaré series (dpeaa)DE-He213 Rook polynomial (dpeaa)DE-He213 Gorenstein algebras (dpeaa)DE-He213 Romeo, Francesco aut Enthalten in Journal of algebraic combinatorics Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992 54(2021), 2 vom: 05. Feb., Seite 607-624 (DE-627)271180722 (DE-600)1479499-8 1572-9192 nnns volume:54 year:2021 number:2 day:05 month:02 pages:607-624 https://dx.doi.org/10.1007/s10801-021-01017-x 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_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_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 54 2021 2 05 02 607-624
allfieldsGer	10.1007/s10801-021-01017-x doi (DE-627)SPR045246114 (SPR)s10801-021-01017-x-e DE-627 ger DE-627 rakwb eng Rinaldo, Giancarlo verfasserin (orcid)0000-0003-3644-1142 aut Hilbert series of simple thin polyominoes 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021 Abstract Let %$\mathcal {P}%$ be a simple thin polyomino, namely a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced Hilbert–Poincaré series %$h(t)/(1-t)^d%$ of %$K[\mathcal {P}]%$ by proving that h(t) is the rook polynomial of %$\mathcal {P}%$. As an application, we characterize the Gorenstein simple thin polyominoes. Simple polyominoes (dpeaa)DE-He213 Hilbert–Poincaré series (dpeaa)DE-He213 Rook polynomial (dpeaa)DE-He213 Gorenstein algebras (dpeaa)DE-He213 Romeo, Francesco aut Enthalten in Journal of algebraic combinatorics Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992 54(2021), 2 vom: 05. Feb., Seite 607-624 (DE-627)271180722 (DE-600)1479499-8 1572-9192 nnns volume:54 year:2021 number:2 day:05 month:02 pages:607-624 https://dx.doi.org/10.1007/s10801-021-01017-x 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_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_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 54 2021 2 05 02 607-624
allfieldsSound	10.1007/s10801-021-01017-x doi (DE-627)SPR045246114 (SPR)s10801-021-01017-x-e DE-627 ger DE-627 rakwb eng Rinaldo, Giancarlo verfasserin (orcid)0000-0003-3644-1142 aut Hilbert series of simple thin polyominoes 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021 Abstract Let %$\mathcal {P}%$ be a simple thin polyomino, namely a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced Hilbert–Poincaré series %$h(t)/(1-t)^d%$ of %$K[\mathcal {P}]%$ by proving that h(t) is the rook polynomial of %$\mathcal {P}%$. As an application, we characterize the Gorenstein simple thin polyominoes. Simple polyominoes (dpeaa)DE-He213 Hilbert–Poincaré series (dpeaa)DE-He213 Rook polynomial (dpeaa)DE-He213 Gorenstein algebras (dpeaa)DE-He213 Romeo, Francesco aut Enthalten in Journal of algebraic combinatorics Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992 54(2021), 2 vom: 05. Feb., Seite 607-624 (DE-627)271180722 (DE-600)1479499-8 1572-9192 nnns volume:54 year:2021 number:2 day:05 month:02 pages:607-624 https://dx.doi.org/10.1007/s10801-021-01017-x 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_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_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 54 2021 2 05 02 607-624
language	English
source	Enthalten in Journal of algebraic combinatorics 54(2021), 2 vom: 05. Feb., Seite 607-624 volume:54 year:2021 number:2 day:05 month:02 pages:607-624
sourceStr	Enthalten in Journal of algebraic combinatorics 54(2021), 2 vom: 05. Feb., Seite 607-624 volume:54 year:2021 number:2 day:05 month:02 pages:607-624
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Simple polyominoes Hilbert–Poincaré series Rook polynomial Gorenstein algebras
isfreeaccess_bool	false
container_title	Journal of algebraic combinatorics
authorswithroles_txt_mv	Rinaldo, Giancarlo @@aut@@ Romeo, Francesco @@aut@@
publishDateDaySort_date	2021-02-05T00:00:00Z
hierarchy_top_id	271180722
id	SPR045246114
language_de	englisch
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author	Rinaldo, Giancarlo
spellingShingle	Rinaldo, Giancarlo misc Simple polyominoes misc Hilbert–Poincaré series misc Rook polynomial misc Gorenstein algebras Hilbert series of simple thin polyominoes
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topic_title	Hilbert series of simple thin polyominoes Simple polyominoes (dpeaa)DE-He213 Hilbert–Poincaré series (dpeaa)DE-He213 Rook polynomial (dpeaa)DE-He213 Gorenstein algebras (dpeaa)DE-He213
topic	misc Simple polyominoes misc Hilbert–Poincaré series misc Rook polynomial misc Gorenstein algebras
topic_unstemmed	misc Simple polyominoes misc Hilbert–Poincaré series misc Rook polynomial misc Gorenstein algebras
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title	Hilbert series of simple thin polyominoes
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title_full	Hilbert series of simple thin polyominoes
author_sort	Rinaldo, Giancarlo
journal	Journal of algebraic combinatorics
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author_browse	Rinaldo, Giancarlo Romeo, Francesco
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author-letter	Rinaldo, Giancarlo
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title_sort	hilbert series of simple thin polyominoes
title_auth	Hilbert series of simple thin polyominoes
abstract	Abstract Let %$\mathcal {P}%$ be a simple thin polyomino, namely a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced Hilbert–Poincaré series %$h(t)/(1-t)^d%$ of %$K[\mathcal {P}]%$ by proving that h(t) is the rook polynomial of %$\mathcal {P}%$. As an application, we characterize the Gorenstein simple thin polyominoes. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021
abstractGer	Abstract Let %$\mathcal {P}%$ be a simple thin polyomino, namely a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced Hilbert–Poincaré series %$h(t)/(1-t)^d%$ of %$K[\mathcal {P}]%$ by proving that h(t) is the rook polynomial of %$\mathcal {P}%$. As an application, we characterize the Gorenstein simple thin polyominoes. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021
abstract_unstemmed	Abstract Let %$\mathcal {P}%$ be a simple thin polyomino, namely a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced Hilbert–Poincaré series %$h(t)/(1-t)^d%$ of %$K[\mathcal {P}]%$ by proving that h(t) is the rook polynomial of %$\mathcal {P}%$. As an application, we characterize the Gorenstein simple thin polyominoes. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021
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title_short	Hilbert series of simple thin polyominoes
url	https://dx.doi.org/10.1007/s10801-021-01017-x
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author2	Romeo, Francesco
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up_date	2024-07-03T14:44:52.879Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR045246114</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230805064709.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">211009s2021 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10801-021-01017-x</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR045246114</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10801-021-01017-x-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Rinaldo, Giancarlo</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0003-3644-1142</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Hilbert series of simple thin polyominoes</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Let %$\mathcal {P}%$ be a simple thin polyomino, namely a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced Hilbert–Poincaré series %$h(t)/(1-t)^d%$ of %$K[\mathcal {P}]%$ by proving that h(t) is the rook polynomial of %$\mathcal {P}%$. As an application, we characterize the Gorenstein simple thin polyominoes.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Simple polyominoes</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hilbert–Poincaré series</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Rook polynomial</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gorenstein algebras</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Romeo, Francesco</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of algebraic combinatorics</subfield><subfield code="d">Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992</subfield><subfield code="g">54(2021), 2 vom: 05. 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