Leírás
Many classical partition identities, such as the Rogers--Ramanujan identities, state that the number of partitions satisfying certain difference conditions equals the number of partitions satisfying certain congruence conditions. Grounded partitions, introduced by Dousse and Konan, are coloured partitions satisfying difference conditions given by a matrix with nonnegative integer entries. For the matrices in this talk, the generating functions are known to be infinite products, corresponding to the principal specialisation of characters of highest weight modules of type A_1^{(1)}. I will present a bijective proof that the generating functions of grounded partitions at level 2 are infinite products. I will then introduce a new combinatorial model for affine crystal graphs of type A_1^{(1)} at level 2, where the vertices are grounded partitions and the arrows are given by explicit bracketing rules.