Garsia--Remmel -rook numbers are not always unimodal
arXiv:2410.19714 · doi:10.1080/10586458.2025.2595005
Abstract
We show by an explicit example that the Garsia--Remmel -rook numbers of Ferrers boards do not all have unimodal sequences of coefficients. This resolves in the negative a question from 1986 by the aforementioned authors.
9 pages. v3: expanded Remark 6, added a table with more examples of q-rook numbers that are not unimodal. Ancillary files include python code to generate examples of q-rook numbers that are not unimodal