Moments of partition statistics, Bell polynomials and Eisenstein-type series
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910271624183808 |
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| author | Kang, Soon-Yi Kim, Byungchan Lee, Chanhee |
| author_facet | Kang, Soon-Yi Kim, Byungchan Lee, Chanhee |
| contents | We develop a systematic method to express generating functions for moments of combinatorial statistics in terms of partition traces. We employ an algebraic approach based on the complete Bell polynomials and their inversion formula, alongside an analytic approach via Faà di Bruno's formula. Our approach can be applied to a wide class of combinatorial statistics, such as the largest part of an integer partition, the partition crank and rank, and the unimodal sequence rank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30801 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Moments of partition statistics, Bell polynomials and Eisenstein-type series Kang, Soon-Yi Kim, Byungchan Lee, Chanhee Combinatorics Number Theory 05A17, 11P81 We develop a systematic method to express generating functions for moments of combinatorial statistics in terms of partition traces. We employ an algebraic approach based on the complete Bell polynomials and their inversion formula, alongside an analytic approach via Faà di Bruno's formula. Our approach can be applied to a wide class of combinatorial statistics, such as the largest part of an integer partition, the partition crank and rank, and the unimodal sequence rank. |
| title | Moments of partition statistics, Bell polynomials and Eisenstein-type series |
| topic | Combinatorics Number Theory 05A17, 11P81 |
| url | https://arxiv.org/abs/2605.30801 |