A new witness identity for 11|p(11n + 6)

Abstract

Let p(n) be the number of partitions of the positive integer n. A new q-series identity is presented which witnesses Ramanujan’s observation that 11|p(11n + 6) for all ≥ at one glance. This identity can be derived in a natural way by applying an algorithm to present subalgebras of the polynomial ring K[z] as K[z]-modules.