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math.CO2000
New Permanent Estimators via Non-Commutative Determinants
Alexander Barvinok
We introduce a new notion of the determinant, called symmetrized determinant, for a square matrix with the entries in an associative algebra . The monomial expansion of the symm…
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…