THE NUMBER OF COMPOSITIONS INTO POWERS OF b
Daniel Krenn, Stephan G. Wagner · 2014
Abstract. For a fixed integer base b ≥ 2, we consider the number of compositions of 1 into a given number of powers of b and, related, the maximum number of representations a positive integer can have as an ordered sum of powers of b. We study the asymptotic growth of those numbers and give precise asymptotic formulae for them, thereby improving on earlier results of Molteni. Our approach uses generating functions, which we obtain from infinite transfer matrices. 1.