Asymptotic enumeration of 0–1 matrices with equal row sums and equal column sums
نویسندگان
چکیده
منابع مشابه
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...
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Let s, t,m, n be positive integers such that sm = tn. Let M(m, s;n, t) be the number of m × n matrices over {0, 1, 2, . . . } with each row summing to s and each column summing to t. Equivalently, M(m, s;n, t) counts 2-way contingency tables of order m× n such that the row marginal sums are all s and the column marginal sums are all t. A third equivalent description is that M(m, s;n, t) is the ...
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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 ...
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Let s = (s1, . . . , sm) and t = (t1, . . . , tn) be vectors of nonnegative integer-valued functions of m,n with equal sum S = ∑m i=1 si = ∑n j=1 tj. Let M(s, t) be the number of m × n matrices with nonnegative integer entries such that the ith row has row sum si and the jth column has column sum tj for all i, j. Such matrices occur in many different settings, an important example being the con...
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Let s, t,m, n be positive integers such that sm = tn. Let M(m, s;n, t) be the number of m × n matrices over {0, 1, 2, . . . } with each row summing to s and each column summing to t. Equivalently, M(m, s;n, t) counts 2-way contingency tables of order m× n such that the row marginal sums are all s and the column marginal sums are all t. A third equivalent description is that M(m, s;n, t) is the ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2003
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(03)00506-8