Congruences for the number of k-tuple partitions with distinct even parts

Abstract

Let k≥1 be an integer and pedk(n) be the number of k-tuple partitions of n wherein even parts are distinct (and odd parts are unrestricted). We prove a class of congruences for pedk(n) mod 2 by Hecke nilpotency. © 2013 Elsevier B.V. All rights reserved.