On asymmetric (0, 1)-matrices with given row and column sum vectors

On nonnegative matrices with given row and column sums

Integral Matrices with Given Row and Column Sums

Let P = (p,,) and Q = (qij) be m x n integral matrices, R and S be integral vectors. Let Nf(R, S) denote the class of all m x n integral matrices A with row sum vector R and column sum vector S satisfying P < A < Q. For a wide variety of classes ‘%$I( R, S) satisfying our main condition, we obtain two necessary and sufficient conditions for the existence of a matrix in @(R, 5). The first charac...

On the Number of Possible Row and Column Sums of 0, 1-Matrices

For n a positive integer, we show that the number of of 2n-tuples of integers that are the row and column sums of some n × n matrix with entries in {0, 1} is evenly divisible by n+1. This confirms a conjecture of Benton, Snow, and Wallach. We also consider a q-analogue for m×n matrices. We give an efficient recursion formula for this analogue. We prove a divisibility result in this context that...

Asymptotic enumeration of sparse 0-1 matrices with irregular row and column sums

Let s = (s1, . . . , sm) and t = (t1, . . . , tn) be vectors of non-negative integervalued functions with equal sum S = ∑m i=1 si = ∑n j=1 tj . Let N(s, t) be the number of m × n matrices with entries from {0, 1} such that the ith row has row sum si and the jth column has column sum tj. Equivalently, N(s, t) is the number of labelled bipartite graphs with degrees of the vertices in one side of ...

Asymptotic Enumeration of Dense 0-1 Matrices with Equal Row Sums and Equal Column Sums

Let s, t,m, n be positive integers such that sm = tn. Let B(m, s;n, t) be the number of m×n matrices over {0, 1} with each row summing to s and each column summing to t. Equivalently, B(m, s;n, t) is the number of semiregular bipartite graphs with m vertices of degree s and n vertices of degree t. Define the density λ = s/n = t/m. The asymptotic value of B(m, s;n, t) has been much studied but t...