5 citations · 13 across the 10 of their papers we have counts for
7 papers · 1 filter
Combinatorial approach to Andrews-Gordon and Bressoud type identities
Jehanne Dousse, Frédéric Jouhet, Isaac Konan
We provide combinatorial tools inspired by work of Warnaar to give combinatorial interpretations of the sum sides of the Andrews-Gordon and Bressoud identities. More precisely, we…
Characters of level standard modules of as generating functions for generalised partitions
Jehanne Dousse, Isaac Konan
We give a new simple formula for the energy function of a level perfect crystal of type introduced by Kang, Kashiwara and Misra. We use this to give several express…
Systematic study of Schmidt-type partitions via weighted words
Isaac Konan
Let be a sequence with elements in a commutative monoid . In this paper, we provide an explicit formula for $$\sum_{\la} C(\la) q^{\sum_{n\ge…
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…
Weighted words at degree two, I: Bressoud's algorithm as an energy transfer
Isaac Konan
In a recent paper, we generalized a partition identity stated by Siladić in his study of the level one standard module of type . The proof used weighted words with an ar…
Generalisations of Capparelli's and Primc's identities, I: coloured Frobenius partitions and combinatorial proofs
Jehanne Dousse, Isaac Konan
In these two companion papers, we give infinite families of partition identities which generalise Primc's and Capparelli's identities, and study their consequences on the theory of…
A bijective proof and generalization of Siladić's Theorem
Isaac Konan
In a recent paper, Dousse introduced a refinement of Siladić's theorem on partitions, where parts occur in two primary and three secondary colors. Her proof used the method of weig…