Stabilization of coefficients for partition polynomials

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© 2014 Walter de Gruyter GmbH, Berlin/Boston. We find that a wide variety of families of partition statistics stabilize in a fashion similar to pk(n), the number of partitions of n with k parts, which satisfies pk(n) = pk+1(n+1), k ≥ n/2. We bound the regions of stabilization, discuss variants on the phenomenon, and give the limiting sequence in many cases as the coefficients of a single-variable generating function. Examples include many statistics that have an Euler product form, partitions with prescribed subsums, and plane overpartitions.

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Integers: Annual Volume 2013