Geodesic
Shuffle-compatible permutation statistics. II: The exterior peak set
Darij Grinberg1
1University of Minnesota, Twin Cities
The electronic journal of combinatorics, Tome 25 (2018) no. 4
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This paper is a continuation of the work "Shuffle-compatible permutation statistics" by Gessel and Zhuang (but can be read independently from the latter). We study the shuffle-compatibility of permutation statistics — a concept introduced by Gessel and Zhuang, 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.
DOI : 10.37236/7946
Classification : 05E05, 05A05, 06A11
Mots-clés : permutations, permutation statistics, shuffles, P-partitions, quasisymmetric functions, algebraic combinatorics

Darij Grinberg  1

1 University of Minnesota, Twin Cities 
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     title = {Shuffle-compatible permutation statistics. {II:} {The} exterior peak set},
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     doi = {10.37236/7946},
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Darij Grinberg. Shuffle-compatible permutation statistics. II: The exterior peak set. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/7946

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