Andrews--Gordon type identities with parity restrictions through particle motion

Abstract

In this paper, we use the particle motion bijection introduced by Warnaar and developed by the two authors, Jouhet and Konan, to study q-series and partition identities of the Andrews--Gordon type with parity restrictions. These restrictions are of the type ``even (resp. odd) parts appear an even number of times". We prove $q$-series identities where a multisum equals a sum of products, which generalise identities of Andrews and Kim--Yee in a similar way that Stanton's identities generalised the Andrews--Gordon identities. As a consequence of our results, we obtain a simple proof of a recent identity of Chern--Li--Stanton--Xue--Yee related to Ariki--Koike algebras.

arXiv comment20 pages, 1 figure