Grounded partitions at level 2 of type A_1^(1) are in size- and length-preserving bijection with odd overpartitions (ground b) and with partitions whose even parts are distinct (ground a).
Periodic Schur process and cylindric partitions
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Periodic Schur process is a generalization of the Schur process introduced in math.CO/0107056. We compute its correlation functions and their bulk scaling limits, and discuss several applications including asymptotic analysis of uniform measures on cylindric partitions, time-dependent extensions of the discrete sine kernel, and bulk limit behavior of certain measures on partitions introduced in hep-th/0306238 in connection with supersymmetric gauge theories.
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$A_1^{(1)}$-Grounded partitions at levels $1$ and $2$, Part I: bijections
Grounded partitions at level 2 of type A_1^(1) are in size- and length-preserving bijection with odd overpartitions (ground b) and with partitions whose even parts are distinct (ground a).