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- W4381573901 abstract "Let $mathcal{P}$ be a frame polyomino, a new kind of non-simple polyomino. In this paper we study the $h$-polynomial of $K[mathcal{P}]$ in terms of the switching rook polynomial of $mathcal{P}$ using the shellable simplicial complex $Delta(mathcal{P})$ attached to $mathcal{P}$. We provide a suitable shelling order for $Delta(mathcal{P})$ in relation to a new combinatorial object, which we call a step of a facet, and we define a bijection between the set of the canonical configuration of $k$ rooks in $mathcal{P}$ and the facets of $Delta(mathcal{P})$ with $k$ steps. Finally we use a famous combinatorial result, due to McMullen and Walkup, about the $h$-vector of a shellable simplicial complex to interpret the $h$-polynomial of $K[mathcal{P}]$ as the switching rook polynomial of $mathcal{P}$." @default.
- W4381573901 created "2023-06-22" @default.
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- W4381573901 date "2023-06-20" @default.
- W4381573901 modified "2023-10-18" @default.
- W4381573901 title "Shellable simplicial complex and switching rook polynomial of frame polyominoes" @default.
- W4381573901 doi "https://doi.org/10.48550/arxiv.2306.11467" @default.
- W4381573901 hasPublicationYear "2023" @default.
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