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math.CO2025
Switching Rook Polynomials of Collections of Cells: Palindromicity and Domino-Stability
Francesco Navarra, Ayesha Asloob Qureshi, Giancarlo Rinaldo
The rook polynomial is a generating function that enumerates the number of ways to place rooks, with no two in the same row or column, on a collection of cells regarded as a pruned…
math.CO2021
Hilbert series of Parallelogram Polyominoes
Ayesha Asloob Qureshi, Giancarlo Rinaldo, Francesco Romeo
We present a conjecture about the reduced Hilbert series of the coordinate ring of a simple polyomino in terms of particular arrangements of non-attacking rooks that can be placed…