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arXiv · 1902.01546

A new encoding of permutations by Laguerre histories

Sherry H. F. Yan·Hao Zhou·Zhicong Lin
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Abstract

We construct a bijection from permutations to some weighted Motzkin paths known as Laguerre histories. As one application of our bijection, a neat $q$-$γ$-positivity expansion of the $(\inv,\exc)$-$q$-Eulerian polynomials is obtained.

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Sherry H. F. Yan, Hao Zhou, Zhicong Lin. 2019-02-05. A new encoding of permutations by Laguerre histories. https://arxiv.org/abs/1902.01546

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