Abstract. Monotone triangles are certain triangular arrays of integers, which correspond to n × n alternating sign matrices when prescribing (1, 2, . . . , n) as bottom row of the monotone triangle. In this article we define halved monotone triangles, a specialization of which correspond to vertically symmetric alternating sign matrices. We derive an operator formula for the number of halved mo...

An Alternating sign matrix is a square matrix of 0’s, 1’s, and −1’s in which the sum of the entries in each row or column is 1 and the signs of the nonzero entries in each row or column alternate. This paper attempts to define an analogue to alternating sign matrices which is infinite and periodic. After showing the analogue we define shares desirable cahracteristics with alternating sign matri...

Let R=(r1, ..., rm) and S=(s1, ..., sn) be nonnegative integral vectors with ; ri=; sj. Let A(R, S) denote the set of all m×n {0, 1}-matrices with row sum vector R and column sum vector S. Suppose A(R, S) ]”. The interchange graph G(R, S) of A(R, S) was defined by Brualdi in 1980. It is the graph with all matrices in A(R, S) as its vertices and two matrices are adjacent provided they differ by ...

We consider the set Σ(R, C) of all m×n matrices having 0-1 entries and prescribed row sums R = (r1, . . . , rm) and column sums C = (c1, . . . , cn). We prove an asymptotic estimate for the cardinality |Σ(R, C)| via the solution to a convex optimization problem. We show that if Σ(R, C) is sufficiently large, then a random matrix D ∈ Σ(R, C) sampled from the uniform probability measure in Σ(R, C...

In a typical MapReduce job, each map task processing one piece of the input file. If two input matrices are stored in separate HDFS files, one map task would not be able to access the two input matrices at the same time. To deal with this problem, we propose a efficient matrix multiplication in Hadoop. For dense matrices, we use plain row major order to store the matrices on HDFS; For sparse ma...

Generalizing the Bruhat order for permutations (so for permutation matrices), a Bruhat order is defined for the class of m by n (0, 1)-matrices with a given row and column sum vector. An algorithm is given for constructing a minimal matrix (with respect to the Bruhat order) in such a class. This algorithm simplifies in the case that the row and column sums are all equal to a constant k. When k ...

We show that the computation of the Popov form of Ore polynomial matrices can be formulated as a problem of computing the left nullspace of such matrices. While this technique is already known for polynomial matrices, the extension to Ore polynomial matrices is not immediate because multiplication of the matrix entries is not commutative. A number of results for polynomial matrices are extended...

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fai...

An increasing number of applications is concerned with recovering a sparsity can be defined in terms of lq balls for q 2 [0, 2), defined as Bq(s) = { v = (vi) 2 R2 : n2 ∑

Orthogonal matrices over arbitrary elds are de ned together with their non-square analogs, which are termed row-orthogonal matrices. Antiorthogonal and self-orthogonal square matrices are introduced together with their non-square analogs. The relationships of these matrices to such codes as self-dual codes and linear codes with complementary duals are given.