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Short proofs of three combinatorial results in the Johnson scheme Linear and matrix generalizations of some combinatorial min-max theorems On hyperbolic corners and unit-area triangles in planar sets of large measure The mex statistic on combinatorial structures On Ending Partizan Subtraction Nim Pairs of square-free arithmetic progressions in infinite words Stotting in positional games Sumsets of random sets A Computational Study of Limited Augmented Zarankiewicz Numbers in the Incidence-Graph Family of Complete Graphs Elementary asymptotics for the Stirling numbers of the second kind: The central range Sharp threshold for Hamilton cycles in randomly perturbed sparse graphs On certain combinatorial expressions of TASEP transition probabilities Diameter Thresholds of Random Cayley Graphs Rowmotion on hook and two-row alt $ν$-Tamari lattices Comparative monotonicity of linear codes by Hermitian and symplectic hull dimensions Tightness of a MaxCut Lower Bound via Vector Chromatic Number 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Understanding the ratio of the partition sum to its Bethe approximation via double covers
Pascal O. Vontobel · 2025-09-24 · via math.CO updates on arXiv.org

For various classes of graphical models it has been observed that the ratio of the partition sum to its Bethe approximation is often close to being the square of the ratio of the partition sum to its degree-2 Bethe approximation. This is of relevance because the latter ratio can often better be analyzed and/or quantified than the former ratio. In this paper, we give some justifications for the observed relationship between these two ratios and then analyze these ratios for two classes of log-supermodular graphical models.