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arXiv · 2508.18461

Universal Matrices for Counting Fibonomial and $C$-nomial Coefficients by their $p$-adic Valuations

Arav Chand
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Abstract

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.

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Arav Chand. 2025-08-25. Universal Matrices for Counting Fibonomial and $C$-nomial Coefficients by their $p$-adic Valuations. https://arxiv.org/abs/2508.18461

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