Geodesic
A counterexample to the shuffle compatiblity conjecture
Ezgi Kantarcı Oğuz1
1UNIVERSITY OF SOUTHERN CALIFORNIA
The electronic journal of combinatorics, Tome 29 (2022) no. 3

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Zbl DOI arXiv
The shuffle product has a connection with several useful permutation statistics such as descent and peak, and corresponds to the multiplication operation in the corresponding descent and peak algebras. Gessel and Zhuang formalized the notion of shuffle-compatibility and studied various permutation statistics from this viewpoint. They further conjectured that any shuffle compatible permutation statistic is a descent statistic. In this note we construct a counter-example to this conjecture.
DOI : 10.37236/10957
Classification : 05A05

Ezgi Kantarcı Oğuz  1

1 UNIVERSITY OF SOUTHERN CALIFORNIA 
Ezgi Kantarcı Oğuz. A counterexample to the shuffle compatiblity conjecture. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/10957
@article{10_37236_10957,
     author = {Ezgi Kantarc{\i} O\u{g}uz},
     title = {A counterexample to the shuffle compatiblity conjecture},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
     number = {3},
     doi = {10.37236/10957},
     zbl = {1498.05009},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10957/}
}
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