We study the properties of the rook complex R of a polyomino P seen as independence complex of a graph G, and the associated Stanley-Reisner ideal IR. In particular, we characterise the polyominoes P having a pure rook complex, and the ones whose Stanley-Reisner ideal has linear resolution. Furthermore, we prove that for a class of polyominoes the Castelnuovo-Mumford regularity of IR coincides with the induced matching number of G.
The Stanley–Reisner ideal of the rook complex of polyominoes
Romeo F.
2024-01-01
Abstract
We study the properties of the rook complex R of a polyomino P seen as independence complex of a graph G, and the associated Stanley-Reisner ideal IR. In particular, we characterise the polyominoes P having a pure rook complex, and the ones whose Stanley-Reisner ideal has linear resolution. Furthermore, we prove that for a class of polyominoes the Castelnuovo-Mumford regularity of IR coincides with the induced matching number of G.File in questo prodotto:
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