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  1. Home > Articles & Issues >
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  3. A Pieri rule for ske ...
Conference paper

A Pieri rule for skew shapes

Sami H. Assaf (1), Peter R. W. Mcnamara
(1) Department of Mathematics [MIT]
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Imported on
January 31, 2017
Published on
December 31, 2009
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Proceedings
DOI
10.46298/dmtcs.2886
License
https://about.hal.science/hal-authorisation-v1
National Science Foundation
0703567
PostDoctoral Research Fellowship
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A Pieri rule for skew shapes

Sami H. Assaf (1), Peter R. W. Mcnamara
(1) Department of Mathematics [MIT]
Abstract
English
The Pieri rule expresses the product of a Schur function and a single row Schur function in terms of Schur functions. We extend the classical Pieri rule by expressing the product of a skew Schur function and a single row Schur function in terms of skew Schur functions. Like the classical rule, our rule involves simple additions of boxes to the original skew shape. Our proof is purely combinatorial and extends the combinatorial proof of the classical case.
French
La règle de Pieri exprime le produit d'une fonction de Schur et de la fonction de Schur d'une seule ligne en termes de fonctions de Schur. Nous étendons la règle classique de Pieri en exprimant le produit d'un fonction gauche de Schur et de la fonction de Schur d'une ligne en termes de fonctions gauches de Schur. Comme la règle classique, notre règle implique l'ajout de cases à la forme gauche initiale. Notre preuve est purement combinatoire et étend celle du cas classique.
Keywords
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • Pieri rule
  • skew Schur functions
  • Robinson-Schensted
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