switchingRookPolynomial -- Switching rook polynomial of a collection of cells
Usage:
switchingRookPolynomial Q
Inputs:
Q, a collection of cells
Outputs:
the switching rook polynomial of Q
Description
The switching rook polynomial encodes the number of switching equivalence classes of rook configurations on a collection of cells $\mathcal{P}$. Each coefficient corresponds to the number of distinct equivalence classes of the chessboard complex modulo the switching rook equivalence relation. Switching rook polynomial appears to describe the Hilbert series of the coordinate ring of collections of cells (see [JN2024], [QRR2022]). Note that when a collection of cells does not contain a square tetromino, then the switching rook polynomial coincides with the rook polynomial.
[JN2024] Shellable simplicial complex and switching rook polynomial of frame polyominoes(R. Jahangir, F. Navarra, 2024, J. Pure Appl. Algebra).
[QRR2022] Hilbert series of parallelogram polyominoes(A.A. Qureshi, R. Rinaldo, F. Romeo, 2022, Res. Math. Sci.).