The number of nonzero binomial coefficients modulo p^alpha
Number Theory
2011-12-14 v3 Combinatorics
Abstract
In 1947 Fine obtained an expression for the number of binomial coefficients on row n of Pascal's triangle that are nonzero modulo p. In this paper we use Kummer's theorem to generalize Fine's theorem to prime powers, expressing the number of nonzero binomial coefficients modulo p^alpha as a sum over certain integer partitions. For fixed alpha, this expression can be rewritten to show explicit dependence on the number of occurrences of each subword in the base-p representation of n.
Cite
@article{arxiv.1001.1783,
title = {The number of nonzero binomial coefficients modulo p^alpha},
author = {Eric Rowland},
journal= {arXiv preprint arXiv:1001.1783},
year = {2011}
}
Comments
10 pages; publication version