Linear time equivalence of Littlewood―Richardson coefficient symmetry maps

Benkart, Sottile, and Stroomer have completely characterized by Knuth and dual Knuth equivalence a bijective proof of the Littlewood―Richardson coefficient conjugation symmetry, i.e. $c_{\mu, \nu}^{\lambda} =c_{\mu^t,\nu^t}^{\lambda ^t}$. Tableau―switching provides an algorithm to produce such a bij...
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Autor*in:	Olga Azenhas [verfasserIn] Alessandro Conflitti [verfasserIn] Ricardo Mamede [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2009

Schlagwörter:	symmetry maps of littlewood―richardson coefficients conjugation symmetry map linearly time reduction of young tableaux bijections tableau―switching schützenberger involution [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]

Übergeordnetes Werk:	In: Discrete Mathematics & Theoretical Computer Science - Discrete Mathematics & Theoretical Computer Science, 2004, (2009), Proceedings
Übergeordnetes Werk:	year:2009 ; number:Proceedings

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.46298/dmtcs.2725

Katalog-ID:	DOAJ097152439

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520			\|a Benkart, Sottile, and Stroomer have completely characterized by Knuth and dual Knuth equivalence a bijective proof of the Littlewood―Richardson coefficient conjugation symmetry, i.e. $c_{\mu, \nu}^{\lambda} =c_{\mu^t,\nu^t}^{\lambda ^t}$. Tableau―switching provides an algorithm to produce such a bijective proof. Fulton has shown that the White and the Hanlon―Sundaram maps are versions of that bijection. In this paper one exhibits explicitly the Yamanouchi word produced by that conjugation symmetry map which on its turn leads to a new and very natural version of the same map already considered independently. A consequence of this latter construction is that using notions of Relative Computational Complexity we are allowed to show that this conjugation symmetry map is linear time reducible to the Schützenberger involution and reciprocally. Thus the Benkart―Sottile―Stroomer conjugation symmetry map with the two mentioned versions, the three versions of the commutative symmetry map, and Schützenberger involution, are linear time reducible to each other. This answers a question posed by Pak and Vallejo.
650		4	\|a symmetry maps of littlewood―richardson coefficients
650		4	\|a conjugation symmetry map
650		4	\|a linearly time reduction of young tableaux bijections
650		4	\|a tableau―switching
650		4	\|a schützenberger involution
650		4	\|a [math.math-co] mathematics [math]/combinatorics [math.co]
650		4	\|a [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
653		0	\|a Mathematics
700	0		\|a Alessandro Conflitti \|e verfasserin \|4 aut
700	0		\|a Ricardo Mamede \|e verfasserin \|4 aut
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matchkey_str	article:13658050:2009----::ierieqiaecoltlworcadocef
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allfields	10.46298/dmtcs.2725 doi (DE-627)DOAJ097152439 (DE-599)DOAJ3839df1e3f224e04b78199a9dcf797f8 DE-627 ger DE-627 rakwb eng QA1-939 Olga Azenhas verfasserin aut Linear time equivalence of Littlewood―Richardson coefficient symmetry maps 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Benkart, Sottile, and Stroomer have completely characterized by Knuth and dual Knuth equivalence a bijective proof of the Littlewood―Richardson coefficient conjugation symmetry, i.e. $c_{\mu, \nu}^{\lambda} =c_{\mu^t,\nu^t}^{\lambda ^t}$. Tableau―switching provides an algorithm to produce such a bijective proof. Fulton has shown that the White and the Hanlon―Sundaram maps are versions of that bijection. In this paper one exhibits explicitly the Yamanouchi word produced by that conjugation symmetry map which on its turn leads to a new and very natural version of the same map already considered independently. A consequence of this latter construction is that using notions of Relative Computational Complexity we are allowed to show that this conjugation symmetry map is linear time reducible to the Schützenberger involution and reciprocally. Thus the Benkart―Sottile―Stroomer conjugation symmetry map with the two mentioned versions, the three versions of the commutative symmetry map, and Schützenberger involution, are linear time reducible to each other. This answers a question posed by Pak and Vallejo. symmetry maps of littlewood―richardson coefficients conjugation symmetry map linearly time reduction of young tableaux bijections tableau―switching schützenberger involution [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] Mathematics Alessandro Conflitti verfasserin aut Ricardo Mamede verfasserin aut In Discrete Mathematics & Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science, 2004 (2009), Proceedings (DE-627)239019105 (DE-600)1412155-4 13658050 nnns year:2009 number:Proceedings https://doi.org/10.46298/dmtcs.2725 kostenfrei https://doaj.org/article/3839df1e3f224e04b78199a9dcf797f8 kostenfrei https://dmtcs.episciences.org/2725/pdf kostenfrei https://doaj.org/toc/1365-8050 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 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_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2009 Proceedings
spelling	10.46298/dmtcs.2725 doi (DE-627)DOAJ097152439 (DE-599)DOAJ3839df1e3f224e04b78199a9dcf797f8 DE-627 ger DE-627 rakwb eng QA1-939 Olga Azenhas verfasserin aut Linear time equivalence of Littlewood―Richardson coefficient symmetry maps 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Benkart, Sottile, and Stroomer have completely characterized by Knuth and dual Knuth equivalence a bijective proof of the Littlewood―Richardson coefficient conjugation symmetry, i.e. $c_{\mu, \nu}^{\lambda} =c_{\mu^t,\nu^t}^{\lambda ^t}$. Tableau―switching provides an algorithm to produce such a bijective proof. Fulton has shown that the White and the Hanlon―Sundaram maps are versions of that bijection. In this paper one exhibits explicitly the Yamanouchi word produced by that conjugation symmetry map which on its turn leads to a new and very natural version of the same map already considered independently. A consequence of this latter construction is that using notions of Relative Computational Complexity we are allowed to show that this conjugation symmetry map is linear time reducible to the Schützenberger involution and reciprocally. Thus the Benkart―Sottile―Stroomer conjugation symmetry map with the two mentioned versions, the three versions of the commutative symmetry map, and Schützenberger involution, are linear time reducible to each other. This answers a question posed by Pak and Vallejo. symmetry maps of littlewood―richardson coefficients conjugation symmetry map linearly time reduction of young tableaux bijections tableau―switching schützenberger involution [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] Mathematics Alessandro Conflitti verfasserin aut Ricardo Mamede verfasserin aut In Discrete Mathematics & Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science, 2004 (2009), Proceedings (DE-627)239019105 (DE-600)1412155-4 13658050 nnns year:2009 number:Proceedings https://doi.org/10.46298/dmtcs.2725 kostenfrei https://doaj.org/article/3839df1e3f224e04b78199a9dcf797f8 kostenfrei https://dmtcs.episciences.org/2725/pdf kostenfrei https://doaj.org/toc/1365-8050 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 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_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2009 Proceedings
allfields_unstemmed	10.46298/dmtcs.2725 doi (DE-627)DOAJ097152439 (DE-599)DOAJ3839df1e3f224e04b78199a9dcf797f8 DE-627 ger DE-627 rakwb eng QA1-939 Olga Azenhas verfasserin aut Linear time equivalence of Littlewood―Richardson coefficient symmetry maps 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Benkart, Sottile, and Stroomer have completely characterized by Knuth and dual Knuth equivalence a bijective proof of the Littlewood―Richardson coefficient conjugation symmetry, i.e. $c_{\mu, \nu}^{\lambda} =c_{\mu^t,\nu^t}^{\lambda ^t}$. Tableau―switching provides an algorithm to produce such a bijective proof. Fulton has shown that the White and the Hanlon―Sundaram maps are versions of that bijection. In this paper one exhibits explicitly the Yamanouchi word produced by that conjugation symmetry map which on its turn leads to a new and very natural version of the same map already considered independently. A consequence of this latter construction is that using notions of Relative Computational Complexity we are allowed to show that this conjugation symmetry map is linear time reducible to the Schützenberger involution and reciprocally. Thus the Benkart―Sottile―Stroomer conjugation symmetry map with the two mentioned versions, the three versions of the commutative symmetry map, and Schützenberger involution, are linear time reducible to each other. This answers a question posed by Pak and Vallejo. symmetry maps of littlewood―richardson coefficients conjugation symmetry map linearly time reduction of young tableaux bijections tableau―switching schützenberger involution [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] Mathematics Alessandro Conflitti verfasserin aut Ricardo Mamede verfasserin aut In Discrete Mathematics & Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science, 2004 (2009), Proceedings (DE-627)239019105 (DE-600)1412155-4 13658050 nnns year:2009 number:Proceedings https://doi.org/10.46298/dmtcs.2725 kostenfrei https://doaj.org/article/3839df1e3f224e04b78199a9dcf797f8 kostenfrei https://dmtcs.episciences.org/2725/pdf kostenfrei https://doaj.org/toc/1365-8050 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 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_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2009 Proceedings
allfieldsGer	10.46298/dmtcs.2725 doi (DE-627)DOAJ097152439 (DE-599)DOAJ3839df1e3f224e04b78199a9dcf797f8 DE-627 ger DE-627 rakwb eng QA1-939 Olga Azenhas verfasserin aut Linear time equivalence of Littlewood―Richardson coefficient symmetry maps 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Benkart, Sottile, and Stroomer have completely characterized by Knuth and dual Knuth equivalence a bijective proof of the Littlewood―Richardson coefficient conjugation symmetry, i.e. $c_{\mu, \nu}^{\lambda} =c_{\mu^t,\nu^t}^{\lambda ^t}$. Tableau―switching provides an algorithm to produce such a bijective proof. Fulton has shown that the White and the Hanlon―Sundaram maps are versions of that bijection. In this paper one exhibits explicitly the Yamanouchi word produced by that conjugation symmetry map which on its turn leads to a new and very natural version of the same map already considered independently. A consequence of this latter construction is that using notions of Relative Computational Complexity we are allowed to show that this conjugation symmetry map is linear time reducible to the Schützenberger involution and reciprocally. Thus the Benkart―Sottile―Stroomer conjugation symmetry map with the two mentioned versions, the three versions of the commutative symmetry map, and Schützenberger involution, are linear time reducible to each other. This answers a question posed by Pak and Vallejo. symmetry maps of littlewood―richardson coefficients conjugation symmetry map linearly time reduction of young tableaux bijections tableau―switching schützenberger involution [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] Mathematics Alessandro Conflitti verfasserin aut Ricardo Mamede verfasserin aut In Discrete Mathematics & Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science, 2004 (2009), Proceedings (DE-627)239019105 (DE-600)1412155-4 13658050 nnns year:2009 number:Proceedings https://doi.org/10.46298/dmtcs.2725 kostenfrei https://doaj.org/article/3839df1e3f224e04b78199a9dcf797f8 kostenfrei https://dmtcs.episciences.org/2725/pdf kostenfrei https://doaj.org/toc/1365-8050 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 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_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2009 Proceedings
allfieldsSound	10.46298/dmtcs.2725 doi (DE-627)DOAJ097152439 (DE-599)DOAJ3839df1e3f224e04b78199a9dcf797f8 DE-627 ger DE-627 rakwb eng QA1-939 Olga Azenhas verfasserin aut Linear time equivalence of Littlewood―Richardson coefficient symmetry maps 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Benkart, Sottile, and Stroomer have completely characterized by Knuth and dual Knuth equivalence a bijective proof of the Littlewood―Richardson coefficient conjugation symmetry, i.e. $c_{\mu, \nu}^{\lambda} =c_{\mu^t,\nu^t}^{\lambda ^t}$. Tableau―switching provides an algorithm to produce such a bijective proof. Fulton has shown that the White and the Hanlon―Sundaram maps are versions of that bijection. In this paper one exhibits explicitly the Yamanouchi word produced by that conjugation symmetry map which on its turn leads to a new and very natural version of the same map already considered independently. A consequence of this latter construction is that using notions of Relative Computational Complexity we are allowed to show that this conjugation symmetry map is linear time reducible to the Schützenberger involution and reciprocally. Thus the Benkart―Sottile―Stroomer conjugation symmetry map with the two mentioned versions, the three versions of the commutative symmetry map, and Schützenberger involution, are linear time reducible to each other. This answers a question posed by Pak and Vallejo. symmetry maps of littlewood―richardson coefficients conjugation symmetry map linearly time reduction of young tableaux bijections tableau―switching schützenberger involution [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] Mathematics Alessandro Conflitti verfasserin aut Ricardo Mamede verfasserin aut In Discrete Mathematics & Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science, 2004 (2009), Proceedings (DE-627)239019105 (DE-600)1412155-4 13658050 nnns year:2009 number:Proceedings https://doi.org/10.46298/dmtcs.2725 kostenfrei https://doaj.org/article/3839df1e3f224e04b78199a9dcf797f8 kostenfrei https://dmtcs.episciences.org/2725/pdf kostenfrei https://doaj.org/toc/1365-8050 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 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_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2009 Proceedings
language	English
source	In Discrete Mathematics & Theoretical Computer Science (2009), Proceedings year:2009 number:Proceedings
sourceStr	In Discrete Mathematics & Theoretical Computer Science (2009), Proceedings year:2009 number:Proceedings
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	symmetry maps of littlewood―richardson coefficients conjugation symmetry map linearly time reduction of young tableaux bijections tableau―switching schützenberger involution [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] Mathematics
isfreeaccess_bool	true
container_title	Discrete Mathematics & Theoretical Computer Science
authorswithroles_txt_mv	Olga Azenhas @@aut@@ Alessandro Conflitti @@aut@@ Ricardo Mamede @@aut@@
publishDateDaySort_date	2009-01-01T00:00:00Z
hierarchy_top_id	239019105
id	DOAJ097152439
language_de	englisch
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callnumber-first	Q - Science
author	Olga Azenhas
spellingShingle	Olga Azenhas misc QA1-939 misc symmetry maps of littlewood―richardson coefficients misc conjugation symmetry map misc linearly time reduction of young tableaux bijections misc tableau―switching misc schützenberger involution misc [math.math-co] mathematics [math]/combinatorics [math.co] misc [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] misc Mathematics Linear time equivalence of Littlewood―Richardson coefficient symmetry maps
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topic_title	QA1-939 Linear time equivalence of Littlewood―Richardson coefficient symmetry maps symmetry maps of littlewood―richardson coefficients conjugation symmetry map linearly time reduction of young tableaux bijections tableau―switching schützenberger involution [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
topic	misc QA1-939 misc symmetry maps of littlewood―richardson coefficients misc conjugation symmetry map misc linearly time reduction of young tableaux bijections misc tableau―switching misc schützenberger involution misc [math.math-co] mathematics [math]/combinatorics [math.co] misc [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] misc Mathematics
topic_unstemmed	misc QA1-939 misc symmetry maps of littlewood―richardson coefficients misc conjugation symmetry map misc linearly time reduction of young tableaux bijections misc tableau―switching misc schützenberger involution misc [math.math-co] mathematics [math]/combinatorics [math.co] misc [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] misc Mathematics
topic_browse	misc QA1-939 misc symmetry maps of littlewood―richardson coefficients misc conjugation symmetry map misc linearly time reduction of young tableaux bijections misc tableau―switching misc schützenberger involution misc [math.math-co] mathematics [math]/combinatorics [math.co] misc [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] misc Mathematics
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title	Linear time equivalence of Littlewood―Richardson coefficient symmetry maps
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title_full	Linear time equivalence of Littlewood―Richardson coefficient symmetry maps
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author_browse	Olga Azenhas Alessandro Conflitti Ricardo Mamede
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title_sort	linear time equivalence of littlewood―richardson coefficient symmetry maps
callnumber	QA1-939
title_auth	Linear time equivalence of Littlewood―Richardson coefficient symmetry maps
abstract	Benkart, Sottile, and Stroomer have completely characterized by Knuth and dual Knuth equivalence a bijective proof of the Littlewood―Richardson coefficient conjugation symmetry, i.e. $c_{\mu, \nu}^{\lambda} =c_{\mu^t,\nu^t}^{\lambda ^t}$. Tableau―switching provides an algorithm to produce such a bijective proof. Fulton has shown that the White and the Hanlon―Sundaram maps are versions of that bijection. In this paper one exhibits explicitly the Yamanouchi word produced by that conjugation symmetry map which on its turn leads to a new and very natural version of the same map already considered independently. A consequence of this latter construction is that using notions of Relative Computational Complexity we are allowed to show that this conjugation symmetry map is linear time reducible to the Schützenberger involution and reciprocally. Thus the Benkart―Sottile―Stroomer conjugation symmetry map with the two mentioned versions, the three versions of the commutative symmetry map, and Schützenberger involution, are linear time reducible to each other. This answers a question posed by Pak and Vallejo.
abstractGer	Benkart, Sottile, and Stroomer have completely characterized by Knuth and dual Knuth equivalence a bijective proof of the Littlewood―Richardson coefficient conjugation symmetry, i.e. $c_{\mu, \nu}^{\lambda} =c_{\mu^t,\nu^t}^{\lambda ^t}$. Tableau―switching provides an algorithm to produce such a bijective proof. Fulton has shown that the White and the Hanlon―Sundaram maps are versions of that bijection. In this paper one exhibits explicitly the Yamanouchi word produced by that conjugation symmetry map which on its turn leads to a new and very natural version of the same map already considered independently. A consequence of this latter construction is that using notions of Relative Computational Complexity we are allowed to show that this conjugation symmetry map is linear time reducible to the Schützenberger involution and reciprocally. Thus the Benkart―Sottile―Stroomer conjugation symmetry map with the two mentioned versions, the three versions of the commutative symmetry map, and Schützenberger involution, are linear time reducible to each other. This answers a question posed by Pak and Vallejo.
abstract_unstemmed	Benkart, Sottile, and Stroomer have completely characterized by Knuth and dual Knuth equivalence a bijective proof of the Littlewood―Richardson coefficient conjugation symmetry, i.e. $c_{\mu, \nu}^{\lambda} =c_{\mu^t,\nu^t}^{\lambda ^t}$. Tableau―switching provides an algorithm to produce such a bijective proof. Fulton has shown that the White and the Hanlon―Sundaram maps are versions of that bijection. In this paper one exhibits explicitly the Yamanouchi word produced by that conjugation symmetry map which on its turn leads to a new and very natural version of the same map already considered independently. A consequence of this latter construction is that using notions of Relative Computational Complexity we are allowed to show that this conjugation symmetry map is linear time reducible to the Schützenberger involution and reciprocally. Thus the Benkart―Sottile―Stroomer conjugation symmetry map with the two mentioned versions, the three versions of the commutative symmetry map, and Schützenberger involution, are linear time reducible to each other. This answers a question posed by Pak and Vallejo.
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Linear time equivalence of Littlewood―Richardson coefficient symmetry maps

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