Row-strict quasisymmetric Schur functions
International audience Haglund, Luoto, Mason, and van Willigenburg introduced a basis for quasisymmetric functions called the $\textit{quasisymmetric Schur function basis}$ which are generated combinatorially through fillings of composition diagrams in much the same way as Schur functions are genera...
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ftccsdartic:oai:HAL:hal-01215042v1 2024-02-11T10:05:14+01:00 Row-strict quasisymmetric Schur functions Mason, Sarah K Remmel, Jeffrey Department of Mathematics Wake Forest University Department of Mathematics Univ California San Diego (MATH - UC San Diego) University of California San Diego (UC San Diego) University of California (UC)-University of California (UC) Bousquet-Mélou Mireille and Wachs Michelle and Hultman Axel Reykjavik, Iceland 2011 https://inria.hal.science/hal-01215042 https://inria.hal.science/hal-01215042/document https://inria.hal.science/hal-01215042/file/dmAO0158.pdf https://doi.org/10.46298/dmtcs.2942 en eng HAL CCSD Discrete Mathematics and Theoretical Computer Science DMTCS info:eu-repo/semantics/altIdentifier/doi/10.46298/dmtcs.2942 hal-01215042 https://inria.hal.science/hal-01215042 https://inria.hal.science/hal-01215042/document https://inria.hal.science/hal-01215042/file/dmAO0158.pdf doi:10.46298/dmtcs.2942 info:eu-repo/semantics/OpenAccess ISSN: 1462-7264 EISSN: 1365-8050 Discrete Mathematics and Theoretical Computer Science 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) https://inria.hal.science/hal-01215042 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.657-668, ⟨10.46298/dmtcs.2942⟩ symmetric and quasisymmetric functions omega operator Schur functions [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] info:eu-repo/semantics/conferenceObject Conference papers 2011 ftccsdartic https://doi.org/10.46298/dmtcs.2942 2024-01-14T01:38:24Z International audience Haglund, Luoto, Mason, and van Willigenburg introduced a basis for quasisymmetric functions called the $\textit{quasisymmetric Schur function basis}$ which are generated combinatorially through fillings of composition diagrams in much the same way as Schur functions are generated through reverse column-strict tableaux. We introduce a new basis for quasisymmetric functions called the $\textit{row-strict quasisymmetric Schur function basis}$ which are generated combinatorially through fillings of composition diagrams in much the same way as Schur functions are generated through row-strict tableaux. We describe the relationship between this new basis and other known bases for quasisymmetric functions, as well as its relationship to Schur polynomials. We obtain a refinement of the omega transform operator as a result of these relationships. Haglund, Luoto, Mason, et van Willigenburg ont introduit une base pour les fonctions quasi-symétriques appelée $\textit{base des fonctions de Schur quasi-symétriques}$, qui sont construites en remplissant des diagrammes de compositions, d'une manière très semblable à la construction des fonctions de Schur à partir des tableaux "column-strict'' (ordre strict sur les colonnes). Nous introduisons une nouvelle base pour les fonctions quasi-symétriques appelée $\textit{base des fonctions de Schur quasi-symétriques "row-strict''}$, qui sont construites en remplissant des diagrammes de compositions, d'une manière très semblable à la construction des fonctions de Schur à partir des tableaux "row-strict'' (ordre strict sur les lignes). Nous décrivons la relation entre cette nouvelle base et d'autres bases connues pour les fonctions quasi-symétriques, ainsi que ses relations avec les polynômes de Schur. Nous obtenons un raffinement de l'opérateur oméga comme conséquence de ces relations. Conference Object Iceland Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) Haglund ENVELOPE(12.180,12.180,65.320,65.320) |
institution |
Open Polar |
collection |
Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
op_collection_id |
ftccsdartic |
language |
English |
topic |
symmetric and quasisymmetric functions omega operator Schur functions [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] |
spellingShingle |
symmetric and quasisymmetric functions omega operator Schur functions [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] Mason, Sarah K Remmel, Jeffrey Row-strict quasisymmetric Schur functions |
topic_facet |
symmetric and quasisymmetric functions omega operator Schur functions [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] |
description |
International audience Haglund, Luoto, Mason, and van Willigenburg introduced a basis for quasisymmetric functions called the $\textit{quasisymmetric Schur function basis}$ which are generated combinatorially through fillings of composition diagrams in much the same way as Schur functions are generated through reverse column-strict tableaux. We introduce a new basis for quasisymmetric functions called the $\textit{row-strict quasisymmetric Schur function basis}$ which are generated combinatorially through fillings of composition diagrams in much the same way as Schur functions are generated through row-strict tableaux. We describe the relationship between this new basis and other known bases for quasisymmetric functions, as well as its relationship to Schur polynomials. We obtain a refinement of the omega transform operator as a result of these relationships. Haglund, Luoto, Mason, et van Willigenburg ont introduit une base pour les fonctions quasi-symétriques appelée $\textit{base des fonctions de Schur quasi-symétriques}$, qui sont construites en remplissant des diagrammes de compositions, d'une manière très semblable à la construction des fonctions de Schur à partir des tableaux "column-strict'' (ordre strict sur les colonnes). Nous introduisons une nouvelle base pour les fonctions quasi-symétriques appelée $\textit{base des fonctions de Schur quasi-symétriques "row-strict''}$, qui sont construites en remplissant des diagrammes de compositions, d'une manière très semblable à la construction des fonctions de Schur à partir des tableaux "row-strict'' (ordre strict sur les lignes). Nous décrivons la relation entre cette nouvelle base et d'autres bases connues pour les fonctions quasi-symétriques, ainsi que ses relations avec les polynômes de Schur. Nous obtenons un raffinement de l'opérateur oméga comme conséquence de ces relations. |
author2 |
Department of Mathematics Wake Forest University Department of Mathematics Univ California San Diego (MATH - UC San Diego) University of California San Diego (UC San Diego) University of California (UC)-University of California (UC) Bousquet-Mélou Mireille and Wachs Michelle and Hultman Axel |
format |
Conference Object |
author |
Mason, Sarah K Remmel, Jeffrey |
author_facet |
Mason, Sarah K Remmel, Jeffrey |
author_sort |
Mason, Sarah K |
title |
Row-strict quasisymmetric Schur functions |
title_short |
Row-strict quasisymmetric Schur functions |
title_full |
Row-strict quasisymmetric Schur functions |
title_fullStr |
Row-strict quasisymmetric Schur functions |
title_full_unstemmed |
Row-strict quasisymmetric Schur functions |
title_sort |
row-strict quasisymmetric schur functions |
publisher |
HAL CCSD |
publishDate |
2011 |
url |
https://inria.hal.science/hal-01215042 https://inria.hal.science/hal-01215042/document https://inria.hal.science/hal-01215042/file/dmAO0158.pdf https://doi.org/10.46298/dmtcs.2942 |
op_coverage |
Reykjavik, Iceland |
long_lat |
ENVELOPE(12.180,12.180,65.320,65.320) |
geographic |
Haglund |
geographic_facet |
Haglund |
genre |
Iceland |
genre_facet |
Iceland |
op_source |
ISSN: 1462-7264 EISSN: 1365-8050 Discrete Mathematics and Theoretical Computer Science 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) https://inria.hal.science/hal-01215042 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.657-668, ⟨10.46298/dmtcs.2942⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/doi/10.46298/dmtcs.2942 hal-01215042 https://inria.hal.science/hal-01215042 https://inria.hal.science/hal-01215042/document https://inria.hal.science/hal-01215042/file/dmAO0158.pdf doi:10.46298/dmtcs.2942 |
op_rights |
info:eu-repo/semantics/OpenAccess |
op_doi |
https://doi.org/10.46298/dmtcs.2942 |
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1790602139086618624 |