An Involution on Semistandard Skyline Fillings
| Autor: | Fan, Neil J. Y., Guo, Peter L., Liu, Nicolas Y. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Non-attacking skyline fillings were used by Haglund, Haiman and Loehr to establish a combinatorial formula for nonsymmetric Macdonald polynomials. Semistandard skyline fillings are non-attacking skyline fillings with both major index and coinversion number equal to zero, which serve as a combinatorial model for key polynomials. In this paper, we construct an involution on semistandard skyline fillings. This involution can be viewed as a vast generalization of the classical Bender--Knuth involution. As an application, we obtain that semistandard skyline fillings are compatible with the Demazure operators, offering a new combinatorial proof that nonsymmetric Macdonald polynomials specialize to key polynomials. Comment: 16 pages |
| Databáze: | arXiv |
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