arXiv Analytics

Sign in

arXiv:1812.11256 [math.CO]AbstractReferencesReviewsResources

Colored partitions and the hooklength formula: partition statistic identities

Emily E. Anible, William J. Keith

Published 2018-12-29Version 1

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.

Comments: Presented by Emily Anible at Integers Conference 2018; submitted to Proceedings
Categories: math.CO
Subjects: 05A17, 11P81
Related articles: Most relevant | Search more
arXiv:1711.02325 [math.CO] (Published 2017-11-07)
Congruences modulo powers of 5 for $k$-colored partitions
arXiv:1705.10067 [math.CO] (Published 2017-05-29)
On a generalized crank for $k$-colored partitions
arXiv:1503.05242 [math.CO] (Published 2015-03-17)
Colored partitions of a convex polygon by noncrossing diagonals