Pattern expansions of permutation statistics
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914238448009216 |
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| author | Cavey, Ian Dennin, Hugh Tenner, Bridget Eileen |
| author_facet | Cavey, Ian Dennin, Hugh Tenner, Bridget Eileen |
| contents | We study the expansions of permutation statistics in the basis of functions counting occurrences of a fixed pattern in a permutation. We show the finiteness of these pattern expansions for a class of permutation statistics including the higher moment statistics, generalizing a result of Berman and Tenner. We also give a combinatorial criterion for the positivity of pattern expansions. Using this criterion, we show that the pattern expansion of the number of reduced words of a permutation is positive and give an enumerative interpretation for the coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03918 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pattern expansions of permutation statistics Cavey, Ian Dennin, Hugh Tenner, Bridget Eileen Combinatorics 05A05 (Primary), 20F55 (Secondary) We study the expansions of permutation statistics in the basis of functions counting occurrences of a fixed pattern in a permutation. We show the finiteness of these pattern expansions for a class of permutation statistics including the higher moment statistics, generalizing a result of Berman and Tenner. We also give a combinatorial criterion for the positivity of pattern expansions. Using this criterion, we show that the pattern expansion of the number of reduced words of a permutation is positive and give an enumerative interpretation for the coefficients. |
| title | Pattern expansions of permutation statistics |
| topic | Combinatorics 05A05 (Primary), 20F55 (Secondary) |
| url | https://arxiv.org/abs/2601.03918 |