Gamma positivity of the Descent based Eulerian polynomial in positive elements of Classical Weyl Groups
| Autor: | Hiranya Kishore Dey, Sivaramakrishnan Sivasubramanian |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Polynomial
Mathematics::Combinatorics Applied Mathematics Eulerian path Theoretical Computer Science Combinatorics symbols.namesake Computational Theory and Mathematics symbols FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics Geometry and Topology Combinatorics (math.CO) Descent (mathematics) Mathematics |
| Popis: | The classical Eulerian polynomials $A_n(t)$ are known to be gamma positive. Define the positive Eulerian polynomial $A_n^+(t)$ as the polynomial obtained when we sum descents over the alternating group. We show that $A_n^+(t)$ is gamma positive iff $n \equiv 0,1$ (mod 4). When $n \equiv 2$ (mod 4) we show that $A_n^+(t)$ can be written as a sum of two gamma positive polynomials while if $n \equiv 3$ (mod 4), we show that $A_n^+(t)$ can be written as a sum of three gamma positive polynomials. Similar results are shown when we consider the positive type-D and type-D Eulerian polynomials. 24 pages |
| Databáze: | OpenAIRE |
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