On two-sided gamma-positivity for simple permutations

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

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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
Issue number2
StatePublished - 8 Jun 2018

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