Unimodality of Partitions in Near-Rectangular Ferrers Diagrams

Abstract

We look at the rank generating function $G_{\lambda }$ of partitions inside the Ferrers diagram of some partition $\lambda$, investigated by Stanton in 1990, as well as a closely related problem investigated by Stanley and Zanello in 2013. We show that $G_{\lambda }$ is not unimodal for a larger class of 4-part partitions than previously known, and also that if the ratios of parts of $\lambda$ are close enough to 1 (depending on how many parts $\lambda$ has), or if the first part is at least half the size of $\lambda$, then $G_{\lambda }$ is unimodal.

arXiv comment15 pages

References in corpus (1)

• Unimodality of partitions with distinct parts inside Ferrers shapes

Cited by in corpus (1)

• Rank Polynomials of Fence Posets are Unimodal