5 papers
Andrews--Gordon type identities with parity restrictions through particle motion
Jehanne Dousse, Jihyeug Jang
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 Andr…
Bailey pairs and quantum -series identites. I. The classical identities
Jehanne Dousse, Jeremy Lovejoy
We use Bailey pairs to prove -series identities at roots of unity due to Cohen and Bryson-Ono-Pitman-Rhoades. The proofs use Bailey pairs with quadratic forms developed in the s…
Andrews--Gordon and Stanton type identities: bijective and Bailey lemma approaches
Jehanne Dousse, Jihyeug Jang, Frédéric Jouhet
In 2018, Stanton proved two types of generalisations of the celebrated Andrews--Gordon and Bressoud identities (in their -series version): one with a similar shape to the origin…
Bilateral Bailey Lattices and Andrews-Gordon Type Identities
Jehanne Dousse, Frédéric Jouhet, Isaac Konan
We show that the Bailey lattice can be extended to a bilateral version in just a few lines from the bilateral Bailey lemma, using a very simple lemma transforming bilateral Bailey…
Partition identities from higher level crystals of
Jehanne Dousse, Leonard Hardiman, Isaac Konan
We study perfect crystals for the standard modules of the affine Lie algebra at all levels using the theory of multi-grounded partitions. We prove a family of partition…