Stabilization of coefficients for partition polynomials

2013/07/04 by Boyer, Robert P., Keith, William J.
#05C15 #15A17 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1307.1418

Abstract

We find that a wide variety of families of partition statistics stabilize in a fashion similar to p_k(n), the number of partitions of n with k parts, which satisfies p_k(n) = p_k+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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