Sign-twisted generating functions of the odd length for Weyl groups of type $D$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912281607012352 |
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| author | Gu, Haihang Yu, Houyi |
| author_facet | Gu, Haihang Yu, Houyi |
| contents | The odd length in Weyl groups is a new statistic analogous to the classical Coxeter length, and features combinatorial and parity conditions. We establish explicit closed product formulas for the sign-twisted generating functions of the odd length for parabolic quotients of Weyl groups of type $D$. As a consequence, we verify three conjectures of Brenti and Carnevale on evaluating closed forms for these generating functions. We then give an equivalent condition for the sign-twisted generating functions to be expressible as products of cyclotomic polynomials, settling a conjecture of Stembridge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_07658 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sign-twisted generating functions of the odd length for Weyl groups of type $D$ Gu, Haihang Yu, Houyi Combinatorics Group Theory 05A15, 05A05, 05E16, 20F55 The odd length in Weyl groups is a new statistic analogous to the classical Coxeter length, and features combinatorial and parity conditions. We establish explicit closed product formulas for the sign-twisted generating functions of the odd length for parabolic quotients of Weyl groups of type $D$. As a consequence, we verify three conjectures of Brenti and Carnevale on evaluating closed forms for these generating functions. We then give an equivalent condition for the sign-twisted generating functions to be expressible as products of cyclotomic polynomials, settling a conjecture of Stembridge. |
| title | Sign-twisted generating functions of the odd length for Weyl groups of type $D$ |
| topic | Combinatorics Group Theory 05A15, 05A05, 05E16, 20F55 |
| url | https://arxiv.org/abs/2303.07658 |