In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m+1} is a re...In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m+1} is a repeated set,W(A) is weight of A.展开更多
We introduce a class of n×n matrices of 0's and l's which can be regarded as generalizations of the classical Ferrets boards of rook theory. Assuming the matrices are fully indecomposable, we determine th...We introduce a class of n×n matrices of 0's and l's which can be regarded as generalizations of the classical Ferrets boards of rook theory. Assuming the matrices are fully indecomposable, we determine the minimum permanent and the minimum numberof l's as a function of n. We also characterize these matrices in terms of weighted,top-rooted trees.展开更多
文摘In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m+1} is a repeated set,W(A) is weight of A.
文摘We introduce a class of n×n matrices of 0's and l's which can be regarded as generalizations of the classical Ferrets boards of rook theory. Assuming the matrices are fully indecomposable, we determine the minimum permanent and the minimum numberof l's as a function of n. We also characterize these matrices in terms of weighted,top-rooted trees.
