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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.01100 |
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| _version_ | 1866917586592071680 |
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| author | Coquereaux, Robert Zuber, Jean-Bernard |
| author_facet | Coquereaux, Robert Zuber, Jean-Bernard |
| contents | We study the enumeration of set partitions, according to their length, number of parts, cyclic type, and genus. We introduce genus-dependent Bell, Stirling numbers, and Faà di Bruno coefficients. Besides attempting to summarize what is already known on the subject, we obtain new generic results (in particular for partitions into two parts, for arbitrary genus), and present computer generated new data extending the number of terms known for sequences or families of such coefficients; this also leads to new conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_01100 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Counting partitions by genus: a compendium of results Coquereaux, Robert Zuber, Jean-Bernard Combinatorics Mathematical Physics 05A18, 05A15, 15B52, 60Cxx We study the enumeration of set partitions, according to their length, number of parts, cyclic type, and genus. We introduce genus-dependent Bell, Stirling numbers, and Faà di Bruno coefficients. Besides attempting to summarize what is already known on the subject, we obtain new generic results (in particular for partitions into two parts, for arbitrary genus), and present computer generated new data extending the number of terms known for sequences or families of such coefficients; this also leads to new conjectures. |
| title | Counting partitions by genus: a compendium of results |
| topic | Combinatorics Mathematical Physics 05A18, 05A15, 15B52, 60Cxx |
| url | https://arxiv.org/abs/2305.01100 |