A basis of the alternating diagonal coinvariants
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915611524726784 |
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| author | Jiang, Yuhan |
| author_facet | Jiang, Yuhan |
| contents | We construct an explicit vector space basis in terms of bivariate Vandermonde determinants for the alternating component of the diagonal coinvariant ring $DR_n$, answering a question of Stump. As a Corollary, we recover the combinatorial formula of the $q,t$-Catalan numbers. Moreover, we construct a decomposition of an $m$-Dyck path into an $m$-tuple of Dyck paths such that the area sequence and bounce sequence of the $m$-Dyck path is entrywise the sum of the area sequences and bounce sequences of the Dyck paths in the tuple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12521 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A basis of the alternating diagonal coinvariants Jiang, Yuhan Combinatorics 05E40 We construct an explicit vector space basis in terms of bivariate Vandermonde determinants for the alternating component of the diagonal coinvariant ring $DR_n$, answering a question of Stump. As a Corollary, we recover the combinatorial formula of the $q,t$-Catalan numbers. Moreover, we construct a decomposition of an $m$-Dyck path into an $m$-tuple of Dyck paths such that the area sequence and bounce sequence of the $m$-Dyck path is entrywise the sum of the area sequences and bounce sequences of the Dyck paths in the tuple. |
| title | A basis of the alternating diagonal coinvariants |
| topic | Combinatorics 05E40 |
| url | https://arxiv.org/abs/2508.12521 |