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arXiv · 1806.04114

Shuffle-compatible permutation statistics II: the exterior peak set

Darij Grinberg
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Abstract

This is a continuation of arXiv:1706.00750 by Gessel and Zhuang (but can be read independently from the latter). We study the shuffle-compatibility of permutation statistics -- a concept introduced in arXiv:1706.00750, although various instances of it have appeared throughout the literature before. We prove that (as Gessel and Zhuang have conjectured) the exterior peak set statistic (Epk) is shuffle-compatible. We furthermore introduce the concept of an "LR-shuffle-compatible" statistic, which is stronger than shuffle-compatibility. We prove that Epk and a few other statistics are LR-shuffle-compatible. Furthermore, we connect these concepts with the quasisymmetric functions, in particular the dendriform structure on them.

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Darij Grinberg. 2018-06-11. Shuffle-compatible permutation statistics II: the exterior peak set. https://doi.org/10.37236/7946

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