Geodesic
On two-sided gamma-positivity for simple permutations
Ron M. Adin1 ; Eli Bagno2 ; Estrella Eisenberg2 ; Shulamit Reches2 ; Moriah Sigron2
1Department of Mathematics, Bar-Ilan University,
2Jerusalem College of Technology
The electronic journal of combinatorics, Tome 25 (2018) no. 2
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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.
DOI : 10.37236/7472
Classification : 05A05, 05A15
Mots-clés : Eulerian polynomials, gamma positivity, valley hopping

Ron M. Adin  1   ; Eli Bagno  2   ; Estrella Eisenberg  2   ; Shulamit Reches  2   ; Moriah Sigron  2

1 Department of Mathematics, Bar-Ilan University,
2 Jerusalem College of Technology 
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Ron M. Adin; Eli Bagno; Estrella Eisenberg; Shulamit Reches; Moriah Sigron. On two-sided gamma-positivity for simple permutations. The electronic journal of combinatorics, Tome 25 (2018) no. 2. doi: 10.37236/7472

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