A combinatorial formula for Interpolation Macdonald polynomials
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908606615519232 |
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| author | Dali, Houcine Ben Williams, Lauren |
| author_facet | Dali, Houcine Ben Williams, Lauren |
| contents | In 1996, Knop and Sahi introduced a remarkable family of inhomogeneous symmetric polynomials, defined via vanishing conditions, whose top homogeneous parts are exactly the Macdonald polynomials. Like the Macdonald polynomials, these interpolation Macdonald polynomials are closely connected to the Hecke algebra, and admit nonsymmetric versions, which generalize the nonsymmetric Macdonald polynomials. In this paper we give a combinatorial formula for interpolation Macdonald polynomials in terms of signed multiline queues; this formula generalizes the combinatorial formula for Macdonald polynomials in terms of multiline queues given by Corteel-Mandelshtam-Williams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02587 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A combinatorial formula for Interpolation Macdonald polynomials Dali, Houcine Ben Williams, Lauren Combinatorics 05E05 In 1996, Knop and Sahi introduced a remarkable family of inhomogeneous symmetric polynomials, defined via vanishing conditions, whose top homogeneous parts are exactly the Macdonald polynomials. Like the Macdonald polynomials, these interpolation Macdonald polynomials are closely connected to the Hecke algebra, and admit nonsymmetric versions, which generalize the nonsymmetric Macdonald polynomials. In this paper we give a combinatorial formula for interpolation Macdonald polynomials in terms of signed multiline queues; this formula generalizes the combinatorial formula for Macdonald polynomials in terms of multiline queues given by Corteel-Mandelshtam-Williams. |
| title | A combinatorial formula for Interpolation Macdonald polynomials |
| topic | Combinatorics 05E05 |
| url | https://arxiv.org/abs/2510.02587 |