Polynomial analogues of restricted multicolor b-ary partition functions

2019/08/10 by Dilcher, Karl, Ericksen, Larry · 1 citation
#11B83 (Secondary) #11P81 (Primary) 11B37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1908.03751

Abstract

Given an integer base b≥ 2, a number ρ≥ 1 of colors, and a finite sequence Λ=(λ₁,…,λ_ρ) of positive integers, we introduce the concept of a Λ-restricted ρ-colored b-ary partition of an integer n≥ 1. We also define a sequence of polynomials in λ₁+⋯+λ_ρ variables, and prove that the nth polynomial characterizes all Λ-restricted ρ-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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• Colored base-3 partitions, sequences of polynomials, and perfect numbers

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