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.