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 language | English |
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Article number | #P2.38 |
Journal | Electronic Journal of Combinatorics |
Volume | 25 |
Issue number | 2 |
DOIs | |
State | Published - 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.
Funders | Funder number |
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MIT-Israel MISTI |