Polynomial Analogues of Restricted b-ary Partition Functions
Department of Mathematics and Statistics
Halifax, NS B3H 4R2
P. O. Box 172
Millville, NJ 08332-0172
Given an integer b ≥ 2, a well studied concept of a b-ary
partition function of a positive integer n counts the number of
representations of n as sums of powers of b, with each
power occurring up to λ times, for a fixed λ ≥ 1.
In this paper we
introduce and study a multivariable polynomial sequence that reduces to
the restricted b-ary partition function when all variables are
taken to be 1. In particular, we show that this polynomial sequence
characterizes all restricted b-ary partitions for each n,
generalizing previous results on hyperbinary and hyper b-ary
representations. All this will follow from considering more general
concepts of restricted b-ary partition functions.
Full version: pdf,
(Concerned with sequences
Received December 2 2018;
revised version received May 8 2019.
Published in Journal of Integer Sequences,
May 17 2019.
Journal of Integer Sequences home page