Apr 14, 2000 · Abstract. Generalizing the notion of placing rooks on a Ferrers board leads to a new class of combinatorial models and a new class of rook ...
In Section 9 we consider generalized rook polynomials associated with partitions of a set, which we call “partition polynomials.” These polynomials may be used ...
Generalizing the notion of placing rooks on a Ferrers board leads to a new class of combinatorial models and a new class of rook polynomials.
In combinatorial mathematics, a rook polynomial is a generating polynomial of the number of ways to place non-attacking rooks on a board that looks like a ...
We consider several generalizations of rook polynomials. In particular we develop analogs of the theory of rook polynomials that are related to general ...
Rook numbers count the number of ways to place non-attacking rooks on a generalized board, and the rook polynomial is a polynomial that organizes the rook ...
One way to generalize the classical 2-dimensional rook polynomial theory to higher dimensions is by letting rooks attack along hyperplanes.
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A rook polynomial is a polynomial R_(m,n)(x)=sum_(k=0)^(min(m,n))r_kx^k (1) whose number of ways k nonattacking rooks can be arranged on an m×n chessboard.
Generalizing the notion of placing rooks on a Ferrers board leads to a new class of combinatorial models and a new class of rook polynomials.
Jan 30, 2013 · They have a multiplicative property: rB(x) = rB1 (x)rB2 (x). Of special interest are the rook polynomials of complete boards: Let ln(x) be the ...