Limit shapes via bijections

Abstract

We compute the limit shape for several classes of restricted integer partitions, where the restrictions are placed on the part sizes rather than the multiplicities. Our approach utilizes certain classes of bijections which map limit shapes continuously in the plane. We start with bijections outlined previously by the second author, and extend them to include limit shapes with different scaling functions.

43 Pages, 8 figures

Cited by in corpus (3)

• Limit shape of minimal difference partitions and fractional statistics
• Poisson approximation for large permutation groups
• Boltzmann Distribution on "Short" Integer Partitions with Power Parts: Limit Laws and Sampling