Colored partitions and the hooklength formula: partition statistic identities
Combinatorics
2019-01-01 v1
Abstract
We give relations between the joint distributions of multiple hook lengths and of frequencies and part sizes in partitions, extending prior work in this area. These results are discovered by investigating truncations of the Han/Nekrasov-Okounkov hooklength formula and of (k,j)-colored partitions, a unification of k-colored partitions and overpartitions. We establish the observed relations at the constant and linear terms for all n, and for j=2 in their quadratic term, with the associated hook/frequency identities. Further results of this type seem likely.
Keywords
Cite
@article{arxiv.1812.11256,
title = {Colored partitions and the hooklength formula: partition statistic identities},
author = {Emily E. Anible and William J. Keith},
journal= {arXiv preprint arXiv:1812.11256},
year = {2019}
}
Comments
Presented by Emily Anible at Integers Conference 2018; submitted to Proceedings