Brunn¿Minkowski inequalities for contingency tables and integer flows

• Autores: Alexander Barvinok
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 211, Nº 1, 2007, págs. 105-122
• Idioma: inglés
• DOI: 10.1016/j.aim.2006.07.012
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• Resumen

  • 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