most citedRandom Weighting, Asymptotic Counting, and Inverse Isoperimetry

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math.CO2003★ 1 cited

Random Weighting, Asymptotic Counting, and Inverse Isoperimetry

Alexander Barvinok, Alex Samorodnitsky

For a family X of k-subsets of the set 1,...,n, let |X| be the cardinality of X and let Gamma(X,mu) be the expected maximum weight of a subset from X when the weights of 1,...,n ar…

math.CO2000

The Distance Approach to Approximate Combinatorial Counting

Alexander Barvinok, Alex Samorodnitsky

We develop general methods to obtain fast (polynomial time) estimates of the cardinality of a combinatorially defined set via solving some randomly generated optimization problems…