Brunn-Minkowski inequalities for contingency tables,integer flows, and related quantities


Alexander Barvinok

University of Michigan

Northeastern University

Thursday, March 15, 2007


Talk at 4:30 p.m. in 509 Lake Hall

Tea at 4:00 p.m. in 544 Nightingale Hall


Abstract:   We discuss a certain approximate log-concavity property for a wide family of combinatorially defined quantities. Examples include the number of non-negative integer matrices (contingency tables) with prescribed row and column sums (margins) as a function of the margins and the number of integer feasible flows in a network, as a function of the excesses at the vertices. Geometrically, we are talking about a version of the Brunn-Minkowski inequality for the number of integer points in a class of polytopes, known as transportation polytopes. This approximate log-concavity results in asymptotic log-concavity under certain natural scaling of parameters and some of the quantities may even be genuinely log-concave. We speculate on possible relations to approximate and genuine log-concavity of constants coming from the representation theory.

Here are some directions to Northeastern University. Lake Hall and Nightingale Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street. The two halls are connected, with no well-defined boundary in between. In particular, 509 Lake Hall is on the same corridor as 544 Nightingale Hall.

There is free parking available for people coming to the Colloquium at Northeastern's visitor parking (Rennaisance Garage). The entrance is from Columbus Avenue. If coming by car, you should park there and take the parking talon. After the lecture, you may pick up the payment coupon from Andrei Zelevinsky.

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Posted:: February 12, 2007    URL: