AbstractThe concept of rook polynomial of a “chessboard” may be generalized to the rook polynomial of an arbitrary rectangular matrix. A conjecture that the rook polynomials of “chessboards” have only real zeros is thus carried over to the rook polynomials of nonnegative matrices. This paper proves these conjectures, and establishes interlacing properties for the zeros of the rook polynomials of a positive matrix and the matrix obtained by striking any one row or any one column
Rook theory is the study of permutations described using terminology from the game of chess. In rook...
The matching polynomial (also called reference and acyclic polynomial) was discovered in chemistry, ...
We study the row-space partition and the pivot partition on the matrix space Fq n×m. We show that bo...
AbstractThe concept of rook polynomial of a “chessboard” may be generalized to the rook polynomial o...
AbstractIn this paper, we find an expression of the rook vector of a matrix A (not necessarily squar...
AbstractWe study the zeros of two families of polynomials related to rook theory and matchings in gr...
AbstractA theorem contained in the paper ‘A combinatoric formula’ by Wang, Lee and Tan (J. Math. Ana...
AbstractCharacterizations are obtained of those linear operators on the m × n matrices over an arbit...
AbstractIn this paper we introduce invisible permutations and rook length polynomials. We prove a re...
In this paper, we studied the game of chess, the rook and its movements to capture pieces in the sam...
AbstractWe give new sufficient conditions for a sequence of polynomials to have only real zeros base...
AbstractGeneralizing the notion of placing rooks on a Ferrers board leads to a new class of combinat...
AbstractThe first section surveys recent results on the permanental polynomial of a square matrix A,...
AbstractIn this paper we provide the first general expressions for the rook and factorial polynomial...
Please note that this paper has been submitted for publication in a journal and is unavailable at th...
Rook theory is the study of permutations described using terminology from the game of chess. In rook...
The matching polynomial (also called reference and acyclic polynomial) was discovered in chemistry, ...
We study the row-space partition and the pivot partition on the matrix space Fq n×m. We show that bo...
AbstractThe concept of rook polynomial of a “chessboard” may be generalized to the rook polynomial o...
AbstractIn this paper, we find an expression of the rook vector of a matrix A (not necessarily squar...
AbstractWe study the zeros of two families of polynomials related to rook theory and matchings in gr...
AbstractA theorem contained in the paper ‘A combinatoric formula’ by Wang, Lee and Tan (J. Math. Ana...
AbstractCharacterizations are obtained of those linear operators on the m × n matrices over an arbit...
AbstractIn this paper we introduce invisible permutations and rook length polynomials. We prove a re...
In this paper, we studied the game of chess, the rook and its movements to capture pieces in the sam...
AbstractWe give new sufficient conditions for a sequence of polynomials to have only real zeros base...
AbstractGeneralizing the notion of placing rooks on a Ferrers board leads to a new class of combinat...
AbstractThe first section surveys recent results on the permanental polynomial of a square matrix A,...
AbstractIn this paper we provide the first general expressions for the rook and factorial polynomial...
Please note that this paper has been submitted for publication in a journal and is unavailable at th...
Rook theory is the study of permutations described using terminology from the game of chess. In rook...
The matching polynomial (also called reference and acyclic polynomial) was discovered in chemistry, ...
We study the row-space partition and the pivot partition on the matrix space Fq n×m. We show that bo...
DOI
Add to ORKG