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arXiv · 2010.08156

An Involution on Semistandard Skyline Fillings

Neil J. Y. Fan·Peter L. Guo·Nicolas Y. Liu
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Abstract

Non-attacking skyline fillings were used by Haglund, Haiman and Loehr to establish a combinatorial formula for nonsymmetric Macdonald polynomials. Semistandard skyline fillings are non-attacking skyline fillings with both major index and coinversion number equal to zero, which serve as a combinatorial model for key polynomials. In this paper, we construct an involution on semistandard skyline fillings. This involution can be viewed as a vast generalization of the classical Bender--Knuth involution. As an application, we obtain that semistandard skyline fillings are compatible with the Demazure operators, offering a new combinatorial proof that nonsymmetric Macdonald polynomials specialize to key polynomials.

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Neil J. Y. Fan, Peter L. Guo, Nicolas Y. Liu. 2020-10-16. An Involution on Semistandard Skyline Fillings. https://arxiv.org/abs/2010.08156

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