Hall polynomials, inverse Kostka polynomials and puzzles

We study two different one-parameter generalizations of Littlewood–Richardson coefficients, namely Hall polynomials and generalized inverse Kostka polynomials, and derive new combinatorial formulae for them. Our combinatorial expressions are closely related to puzzles, originally introduced by Knuts...

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Bibliographic Details
Published inJournal of combinatorial theory. Series A Vol. 159; pp. 107 - 163
Main Authors Wheeler, M., Zinn-Justin, P.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.10.2018
Subjects
Integrable lattice models
Littlewood–Richardson coefficients
Symmetric functions
Integrable lattice models
Symmetric functions
Littlewood–Richardson coefficients
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Summary:We study two different one-parameter generalizations of Littlewood–Richardson coefficients, namely Hall polynomials and generalized inverse Kostka polynomials, and derive new combinatorial formulae for them. Our combinatorial expressions are closely related to puzzles, originally introduced by Knutson and Tao in their work on the equivariant cohomology of the Grassmannian.
ISSN:0097-3165
1096-0899
DOI:10.1016/j.jcta.2018.05.005