Macdonald symmetry at $q=1$ and a new class of inv-preserving bijections on words
| Autor: | Gillespie, Maria, Kaliszewski, Ryan, Morse, Jennifer |
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| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We give a direct combinatorial proof of the $q,t$-symmetry relation $\tilde H_{\mu}(X;q,t)=\tilde H_{\mu'}(X;t,q)$ in the Macdonald polynomials $\tilde H_\mu$ at the specialization $q=1$. The bijection demonstrates that the Macdonald inv statistic on the permutations of any given row of a Young diagram filling is Mahonian. Moreover, our bijection gives rise a family of new bijections on words that preserves the classical Mahonian inv statistic. Comment: 10 pages; submitted to FPSAC 2017 |
| Databáze: | arXiv |
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