Lower Bounds for Multivariate Independence Polynomials

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combinatoricsAug 5, 2026Significance 12/100Registry: lean checked

Lower Bounds for Multivariate Independence Polynomials

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The multivariate independence polynomial is the partition function of the hard-core model with per-vertex fugacities. The paper proves a lower bound extending to the multivariate setting a result Tao proved in the univariate case, and settles a conjectured generalization for a multiaffine version of the semiproper colouring partition function with two proper colours.

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The multivariate independence polynomial is the partition function of the hard-core model with per-vertex fugacities. The paper proves a lower bound extending to the multivariate setting a result Tao proved in the univariate case, and settles a conjectured generalization for a multiaffine version of the semiproper colouring partition function with two proper colours.

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