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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2016
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1605.03524 |
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| _version_ | 1866909036488687616 |
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| author | Barnard, Emily Reading, Nathan |
| author_facet | Barnard, Emily Reading, Nathan |
| contents | We pose counting problems related to the various settings for Coxeter-Catalan combinatorics (noncrossing, nonnesting, clusters, Cambrian). Each problem is to count "twin" pairs of objects from a corresponding problem in Coxeter-Catalan combinatorics. We show that the problems all have the same answer, and, for a given finite Coxeter group W, we call the common solution to these problems the W-biCatalan number. We compute the W-biCatalan number for all W and take the first steps in the study of Coxeter-biCatalan combinatorics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1605_03524 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Coxeter-biCatalan combinatorics Barnard, Emily Reading, Nathan Combinatorics We pose counting problems related to the various settings for Coxeter-Catalan combinatorics (noncrossing, nonnesting, clusters, Cambrian). Each problem is to count "twin" pairs of objects from a corresponding problem in Coxeter-Catalan combinatorics. We show that the problems all have the same answer, and, for a given finite Coxeter group W, we call the common solution to these problems the W-biCatalan number. We compute the W-biCatalan number for all W and take the first steps in the study of Coxeter-biCatalan combinatorics. |
| title | Coxeter-biCatalan combinatorics |
| topic | Combinatorics |
| url | https://arxiv.org/abs/1605.03524 |