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arXiv · 1908.03751

Polynomial analogues of restricted multicolor b-ary partition functions

Karl Dilcher·Larry Ericksen
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Abstract

Given an integer base $b\geq 2$, a number $\rho\geq 1$ of colors, and a finite sequence $\Lambda=(\lambda_1,\ldots,\lambda_\rho)$ of positive integers, we introduce the concept of a $\Lambda$-restricted $\rho$-colored $b$-ary partition of an integer $n\geq 1$. We also define a sequence of polynomials in $\lambda_1+\cdots+\lambda_\rho$ variables, and prove that the $n$th polynomial characterizes all $\Lambda$-restricted $\rho$-colored $b$-ary partitions of $n$. In the process we define a recurrence relation for the polynomials in question, obtain explicit formulas and identify a factorization theorem.

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Karl Dilcher, Larry Ericksen. 2019-08-10. Polynomial analogues of restricted multicolor b-ary partition functions. https://arxiv.org/abs/1908.03751

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