Universal Matrices for Counting Fibonomial and $C$-nomial Coefficients by their $p$-adic Valuations
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912554636279808 |
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| author | Chand, Arav |
| author_facet | Chand, Arav |
| contents | Rowland found a matrix product formula for generating functions counting binomial coefficients by their $p$-adic valuations. A natural generalization of binomial coefficients was introduced by Knuth and Wilf defined by a sequence $C$. We obtain analogous matrix product formulas counting these $C$-nomial coefficients when $C$ is a strong divisibility sequence. Surprisingly, the matrices are universal in the sense that they are independent of $C$. We further extend this product to $C$-multinomial coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18461 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Matrices for Counting Fibonomial and $C$-nomial Coefficients by their $p$-adic Valuations Chand, Arav Number Theory Combinatorics 11B65, 05A15 (Primary) 11F33, 11B39, 68R15 (Secondary) Rowland found a matrix product formula for generating functions counting binomial coefficients by their $p$-adic valuations. A natural generalization of binomial coefficients was introduced by Knuth and Wilf defined by a sequence $C$. We obtain analogous matrix product formulas counting these $C$-nomial coefficients when $C$ is a strong divisibility sequence. Surprisingly, the matrices are universal in the sense that they are independent of $C$. We further extend this product to $C$-multinomial coefficients. |
| title | Universal Matrices for Counting Fibonomial and $C$-nomial Coefficients by their $p$-adic Valuations |
| topic | Number Theory Combinatorics 11B65, 05A15 (Primary) 11F33, 11B39, 68R15 (Secondary) |
| url | https://arxiv.org/abs/2508.18461 |