Brunn–Minkowski inequalities for contingency tables and integer flows
Brunn–Minkowski inequalities for contingency tables and integer flows
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列联表和整数流的 Brunn–Minkowski 不等式
DOI：
10.1016/j.aim.2006.07.012
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发表时间：
2006
影响因子：
1.7
通讯作者：
A. Barvinok
中科院分区：
文献类型：
--
作者：
A. Barvinok
我们建立了一大类组合定义的整数值函数的近似对数凹性。示例包括具有规定行和列和（边距）的非负整数矩阵（列联表）的数量，作为边距的函数，以及网络中整数可行流的数量，作为顶点过剩的函数。作为推论，我们得到了a型的Kostant配分函数的近似对数凹性。我们还提出了一个间接证据，证明至少一些考虑的函数可能是真正的对数凹性。
We establish approximate log-concavity for a wide family of combinatorially defined integer-valued functions. 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. As a corollary, we obtain approximate log-concavity for the Kostant partition function of type A. We also present an indirect evidence that at least some of the considered functions might be genuinely log-concave.