Hall polynomials, inverse Kostka polynomials and puzzles

M Wheeler; P Zinn-Justin

Journal article

Hall polynomials, inverse Kostka polynomials and puzzles

M Wheeler, P Zinn-Justin

Journal of Combinatorial Theory Series A | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2018

DOI: 10.1016/j.jcta.2018.05.005

Abstract

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.

University of Melbourne Researchers

Michael Wheeler Author

Paul Zinn-Justin Author

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Grants

Awarded by Seventh Framework Programme

Funding Acknowledgements

MW is supported by the Australian Research Council grant DE160100958 and the ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS). MW would like to thank Eric Ragoucy for kind hospitality and stimulating discussions at the Laboratoire d'Annecy-le-Vieux de Physique Theorique (LAPTh), while this manuscript was in preparation. PZJ is supported by ERC grant "LIC" 278124, Australian Research Council grants DP140102201 and FT150100232.