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arXiv · 1703.03088

A major-index preserving map on fillings

Per Alexandersson·Mehtaab Sawhney
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Abstract

We generalize a map by S. Mason regarding two combinatorial models for key polynomials, in a way that accounts for the major index. We also define similar variants of this map, that regards alternative models for the modified Macdonald polynomials at $t=0$, thus partially answer a question by J. Haglund. These maps imply certain uniqueness property regarding inversion-- and coinversion-free fillings, which allows us to generalize the notion of charge to a non-symmetric setting, thus answering a question by A. Lascoux. The analogous question in the symmetric setting proves a conjecture by K. Nelson.

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Per Alexandersson, Mehtaab Sawhney. 2017-03-21. A major-index preserving map on fillings. https://arxiv.org/abs/1703.03088

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