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math.CO2010★ 9 cited
The number of graphs and a random graph with a given degree sequence
Alexander Barvinok, J. A. Hartigan
We consider the set of all graphs on n labeled vertices with prescribed degrees D=(d_1, ..., d_n). For a wide class of tame degree sequences D we prove a computationally efficient…
math.CO2009★ 8 cited
An asymptotic formula for the number of non-negative integer matrices with prescribed row and column sums
Alexander Barvinok, J. A. Hartigan
We count mxn non-negative integer matrices (contingency tables) with prescribed row and column sums (margins). For a wide class of smooth margins we establish a computationally eff…