Garsia--Remmel q-劣 rook 数并非总是单调
组合数学
2026-02-19 v3
摘要
我们通过一个具体例子展示，Ferrers 板块的 Garsia--Remmel q-劣 rook 数的系数序列并非都具有单调性。这否定了该作者于1986年提出的此类问题。
引用
@article{arxiv.2410.19714,
title = {Garsia--Remmel $q$-rook numbers are not always unimodal},
author = {Joel Brewster Lewis and Alejandro H. Morales},
journal= {arXiv preprint arXiv:2410.19714},
year = {2026}
}
备注
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