On two-sided gamma-positivity for simple permutations
| Autor: | Shulamit Reches, Eli Bagno, Ron M. Adin, Moriah Sigron, Estrella Eisenberg |
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| Rok vydání: | 2017 |
| Předmět: |
Polynomial
0102 computer and information sciences 01 natural sciences Theoretical Computer Science Combinatorics Permutation symbols.namesake Integer Simple (abstract algebra) FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics 0101 mathematics Descent (mathematics) Mathematics Conjecture Mathematics::Combinatorics Applied Mathematics 010102 general mathematics Substitution (logic) Eulerian path Computational Theory and Mathematics 010201 computation theory & mathematics 05E18 symbols Geometry and Topology Combinatorics (math.CO) |
| DOI: | 10.48550/arxiv.1711.06511 |
| Popis: | 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. Comment: 10 pages, 2 figures |
| Databáze: | OpenAIRE |
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