On the Schur Positivity of $\Delta_{e_2} e_n[X]$
| Autor: | Emily Sergel, Jeffrey B. Remmel, Guoce Xin, Qiu Dun |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Polynomial (hyperelastic model)
Mathematics::Combinatorics Applied Mathematics Function (mathematics) Delta operator Lambda Theoretical Computer Science Combinatorics Computational Theory and Mathematics Macdonald polynomials Mathematics - Combinatorics Discrete Mathematics and Combinatorics Geometry and Topology Mathematics |
| Zdroj: | The Electronic Journal of Combinatorics. 25 |
| ISSN: | 1077-8926 |
| DOI: | 10.37236/7494 |
| Popis: | Let $\mathbb{N}$ denote the set of non-negative integers. Haglund, Wilson, and the second author have conjectured that the coefficient of any Schur function $s_\lambda[X]$ in $\Delta_{e_k} e_n[X]$ is a polynomial in $\mathbb{N}[q,t]$. We present four proofs of a stronger statement in the case $k=2$; We show that the coefficient of any Schur function $s_\lambda[X]$ in $\Delta_{e_2} e_n[X]$ has a positive expansion in terms of $q,t$-analogs. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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