Congruence classes of 2-adic valuations of Stirling numbers of the second kind

Abstract

We analyze congruence classes of $S(n,k)$, the Stirling numbers of the second kind, modulo powers of 2. This analysis provides insight into a conjecture posed by Amdeberhan, Manna and Moll, which those authors established for $k\le 5$. We provide a framework that can be used to justify the conjecture by computational means, which we then complete for $k=5,6,...,20$.

23 pages, 1 figure

Cited by in corpus (2)

• A note on $p$-adic locally analytic functions with application to behavior of the $p$-adic valuations of Stirling numbers
• Divisibility by 2 of Stirling numbers of the second kind and their differences