Showing math.COShow all
3 papers · 1 filter
math.CO2009
Rationality of generating functions of rook polynomials and permanents of Kronecker products of Toeplitz matrices and circulants with the matrix and their evaluation. I
A. M. Kamenetskii
In this paper we give a generalization created by the author of the theory of rook polynomials and permanents of circulants, Toeplits matrices and their submatrices.
math.CO2009
Determinants and permanents of an arbitrary Hadamard degree of a Cauchy matrix and a proof of a generalization of a conjecture of R.F.Scott (1881)
A. M. Kamenetskii
In this paper we give the absolutely new proof of a conjecture of R.F.Scott(1881) on the permanent of a Cauchy matrix $\ls \frac{1}{x_i-y_j} \rs_{1 \leqslant i,j \leqslant n},$ whe…
math.CO2009
Basics of the theory of cyclic rook polynomials and cyclic permanents of rectangular matrices
A. M. Kamenetskii
Combinatorial formulas expressing cyclic rook polynomials and cyclic permanents of rectangular matrices in terms of expansions along rows are presented