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.
From: Darij Grinberg [view email]
[v1]
Mon, 11 Jun 2018 17:27:22 UTC (876 KB)
[v2]
Mon, 18 Jun 2018 22:09:13 UTC (1,059 KB)
[v3]
Sun, 7 Oct 2018 03:03:39 UTC (1,068 KB)
[v4]
Tue, 1 Sep 2026 04:10:24 UTC (1,090 KB)
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