We define a higher spin alternating sign matrix to be an integer-entry square matrix in which, for a nonnegative integer r, all complete row and column sums are r, and all partial row and column sums extending from each end of the row or column are nonnegative. Such matrices correspond to configurations of spin r/2 statistical mechanical vertex models with domain-wall boundary conditions. The c...

In this paper, the eigenvalues of row-inverted 2 × 2 Sylvester Hadamard matrices are derived. Especially when the sign of a single row or two rows of a 2×2 Sylvester Hadamard matrix are inverted, its eigenvalues are completely evaluated. As an example, we completely list all the eigenvalues of 256 different row-inverted Sylvester Hadamard matrices of size 8. Mathematics Subject Classification (...

Abstract. Let Mn;m be the set of n-by-m matrices with entries inthe field of real numbers. A matrix R in Mn = Mn;n is a generalizedrow substochastic matrix (g-row substochastic, for short) if Re e, where e = (1; 1; : : : ; 1)t. For X; Y 2 Mn;m, X is said to besgut-majorized by Y (denoted by X sgut Y ) if there exists ann-by-n upper triangular g-row substochastic matrix R such thatX = RY . This ...

It is proved that a certain symmetric sequence (h0, h1, . . . , hd) of nonnegative integers arising in the enumeration of magic squares of given size n by row sums or, equivalently, in the generating function of the Ehrhart polynomial of the polytope of doubly stochastic n × n matrices, is equal to the h-vector of a simplicial polytope and hence that it satisfies the conditions of the g-theorem...

In this paper, based on the numerical relationship between row and column sums, an equivalent representation for double α1-matrices is given by partition of the row and column index sets. As its application, we obtain a subclass of H-matrices and the corresponding (Cassini-type) spectral distribution theorem. And then, we provide a numerical example to illustrates the effectiveness of the new r...

Abstract We derive a novel stochastic representation of exchangeable Marshall–Olkin distributions based on their death-counting processes. show that these processes are Markov. Furthermore, we provide numerically stable approximation infinitesimal generator matrices in the extendible case. This approach uses integral representations Bernstein functions to calculate generator’s first row, and th...

In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of 2¥2 stochastic matrices are found explicitly. A method based on characteristic polynomial of matrix is developed to find all real root matrices that are functions of the original 3¥3 matrix, including all possible (function) stochastic root matrices. In addition, we comment on some numerical met...

We derive expressions for the average distance distributions in several ensembles of regular low-density parity-check codes (LDPC). Among these ensembles are the standard one defined by matrices having given column and row sums, ensembles defined by matrices with given column sums or given row sums, and an ensemble defined by bipartite graphs.

The n Birkhoff polytope is the set of all doubly stochastic n × n matrices, that is, those matrices with nonnegative real coefficients in which every row and column sums to one. A wide open problem concerns the volumes of these polytopes, which have been known for n ≤ 8. We present a new, complex-analytic way to compute the Ehrhart polynomial of the Birkhoff polytope, that is, the function coun...