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arXiv · 2410.19714

Garsia--Remmel $q$-rook numbers are not always unimodal

Joel Brewster Lewis·Alejandro H. Morales
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Abstract

We show by an explicit example that the Garsia--Remmel $q$-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.

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Joel Brewster Lewis, Alejandro H. Morales. 2026-02-18. Garsia--Remmel $q$-rook numbers are not always unimodal. https://doi.org/10.1080/10586458.2025.2595005

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