Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes
Abstract Some new relations on skew Schur function differences are established both combinatorially using Schützenberger’s jeu de taquin, and algebraically using Jacobi-Trudi determinants. These relations lead to the conclusion that certain differences of skew Schur functions are Schur positive. App...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
King, Ronald C. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2007 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, LLC 2007 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of algebraic combinatorics - Springer US, 1992, 28(2007), 1 vom: 21. Dez., Seite 139-167 |
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| Übergeordnetes Werk: |
volume:28 ; year:2007 ; number:1 ; day:21 ; month:12 ; pages:139-167 |
| Links: |
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| DOI / URN: |
10.1007/s10801-007-0113-0 |
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OLC2034247124 |
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| 520 | |a Abstract Some new relations on skew Schur function differences are established both combinatorially using Schützenberger’s jeu de taquin, and algebraically using Jacobi-Trudi determinants. These relations lead to the conclusion that certain differences of skew Schur functions are Schur positive. Applying these results to a basis of symmetric functions involving ribbon Schur functions confirms the validity of a Schur positivity conjecture due to McNamara. A further application reveals that certain differences of products of Schubert classes are Schubert positive. | ||
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Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes |
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Abstract Some new relations on skew Schur function differences are established both combinatorially using Schützenberger’s jeu de taquin, and algebraically using Jacobi-Trudi determinants. These relations lead to the conclusion that certain differences of skew Schur functions are Schur positive. Applying these results to a basis of symmetric functions involving ribbon Schur functions confirms the validity of a Schur positivity conjecture due to McNamara. A further application reveals that certain differences of products of Schubert classes are Schubert positive. © Springer Science+Business Media, LLC 2007 |
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Abstract Some new relations on skew Schur function differences are established both combinatorially using Schützenberger’s jeu de taquin, and algebraically using Jacobi-Trudi determinants. These relations lead to the conclusion that certain differences of skew Schur functions are Schur positive. Applying these results to a basis of symmetric functions involving ribbon Schur functions confirms the validity of a Schur positivity conjecture due to McNamara. A further application reveals that certain differences of products of Schubert classes are Schubert positive. © Springer Science+Business Media, LLC 2007 |
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Abstract Some new relations on skew Schur function differences are established both combinatorially using Schützenberger’s jeu de taquin, and algebraically using Jacobi-Trudi determinants. These relations lead to the conclusion that certain differences of skew Schur functions are Schur positive. Applying these results to a basis of symmetric functions involving ribbon Schur functions confirms the validity of a Schur positivity conjecture due to McNamara. A further application reveals that certain differences of products of Schubert classes are Schubert positive. © Springer Science+Business Media, LLC 2007 |
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Welsh, Trevor A. van Willigenburg, Stephanie J. |
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10.1007/s10801-007-0113-0 |
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2024-07-03T20:14:47.241Z |
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