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arXiv · 1909.10720

Honeycombs for Hall polynomials

Paul Zinn-Justin
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Abstract

We propose a new formulation of Hall polynomials in terms of honeycombs, which were previously introduced in the context of the Littlewood--Richardson rule. We prove a Pieri rule and associativity for our honeycomb formula, thus showing equality with Hall polynomials. Our proofs are linear algebraic in nature, extending nontrivially the corresponding bijective results for ordinary Littlewood--Richardson coefficients [A. Knutson, T. Tao, C. Woodward, 2004].

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Paul Zinn-Justin. 2020-02-04. Honeycombs for Hall polynomials. https://arxiv.org/abs/1909.10720

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