On two-sided gamma-positivity for simple permutations

Ron M. Adin, Eli Bagno, Estrella Eisenberg, Shulamit Reches, Moriah Sigron

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4 Scopus citations

Abstract

Gessel conjectured that the two-sided Eulerian polynomial, recording the common distribution of the descent number of a permutation and that of its inverse, has non-negative integer coefficients when expanded in terms of the gamma basis. This conjecture has been proved recently by Lin. We conjecture that an analogous statement holds for simple permutations, and use the substitution decomposition tree of a permutation (by repeated inflation) to show that this would imply the Gessel-Lin result. We provide supporting evidence for this stronger conjecture.

Original languageEnglish
Article number#P2.38
JournalElectronic Journal of Combinatorics
Volume25
Issue number2
DOIs
StatePublished - 8 Jun 2018

Bibliographical note

Publisher Copyright:
© The author. Released under the CC BY license (International 4.0).

Funding

The authors thank Mathilde Bouvel and an anonymous referee for useful comments. RMA thanks the Institute for Advanced Studies, Jerusalem, for its hospitality during part of the work on this paper. Work of RMA was partially supported by an MIT-Israel MISTI grant.

FundersFunder number
MIT-Israel MISTI

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