A 0, \1 matrix is balanced if, in every square submatrix with two nonzero entries per row and column, the sum of the entries is a multiple of four. This paper extends the decomposition of balanced 0, 1 matrices obtained by Conforti, Cornue jols, and Rao (1999, J. Combin. Theory Ser. B 77, 292 406) to the class of balanced 0, \1 matrices. As a consequence, we obtain a polynomial time algorithm f...

Judice and Pires developed in recent years principal pivoting methods for the solving of the so-called box linear complementarity problems (BLCPs) where the constraint matrices are restrictedly supposed to be of P–matrices. This paper aims at presenting a new principal pivoting scheme for BLCPs where the constraint matrices are loosely supposed to be row sufficient. This scheme can be applied t...

Abstract: Infinite–dimensional linear dynamic systems described by infinite matrices are studied. Approximate controllability for systems with lower-diagonal matrices is investigated, whereas observability is studied for systems with row-finite and upper-diagonal matrices. Different necessary or sufficient conditions of approximate controllability and observability of such systems are given. Th...

Abstract. In the early 1980s, Mills, Robbins and Rumsey conjectured, and in 1996 Zeilberger proved a simple product formula for the number of n × n alternating sign matrices with a 1 at the top of the i-th column. We give an alternative proof of this formula using our operator formula for the number of monotone triangles with prescribed bottom row. In addition, we provide the enumeration of cer...

We discuss implementing blocked sparse matrix-vector multiplication for NVIDIA GPUs. We outline an algorithm and various optimizations, and identify potential future improvements and challenging tasks. In comparison with previously published implementation, our implementation is faster on matrices having many high fill-ratio blocks but slower on matrices with low number of non-zero elements per...

A lonesum matrix is a (0, 1)-matrix uniquely determined by its column and row sums, and the sum of its all entries is called the “weight” of it. The generating function of numbers of weighted lonesum matrices of each weight is given. A certain explicit formula for the number of weighted lonesum matrices is also proved.

Q0: (Do Not Hand This In) Consider a (simultaneous-move) two-person game described by two m × n matrices R and C that specify respectively, the payoffs to the row player and the column player. That is, (R,C) describes a two-person game where the row and column players have m and n strategies respectively, and Rij and Cij are the payoffs to the row and column players respectively when the row pl...

We count m×n non-negative integer matrices (contingency tables) with prescribed row and column sums (margins). For a wide class of smooth margins we establish a computationally efficient asymptotic formula approximating the number of matrices within a relative error which approaches 0 as m and n grow.

In this paper, we provide an asymptotic for the number of row-Fishburn matrices of size n which settles a conjecture by Vit Jeĺınek. Additionally, using q-series constructions we provide new identities for the generating functions for the number of such matrices, one of which was conjectured by Peter Bala.

A normalized Hadamard matrix is said to be completely noncyclic if no two row vectors are shift equivalent in its punctured matrix (i.e., with the first column removed). In this paper we present an infinite recursive construction for completely noncyclic quaternary Hadamard matrices. These Hadamard matrices are useful in constructing low correlation zone sequences.