Strict log-concavity of the Kirchhoff polynomial and its applications to the strong Lefschetz property

Nagaoka, Takahiro; Yazawa, Akiko

doi:10.1016/j.jalgebra.2021.01.037

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Proof Contraction and Deletion Of An Edge Show That1

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2021

2024

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Cited by 4 publications

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“…E y/ D E y E v T is linear. Together with the well-known log-concavity of matroid polynomials [1,87], it can be shown that the function . E y/ is also log-concave within each tree sector.…”

Section: Proof Contraction and Deletion Of An Edge Show Thatmentioning

confidence: 98%

Hepp’s bound for Feynman graphs and matroids

Panzer¹

2022

Ann. Inst. Henri Poincaré Comb. Phys. Interact.

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We study a rational matroid invariant, obtained as the tropicalization of the Feynman period integral. It equals the volume of the polar of the matroid polytope and we give efficient formulas for its computation. This invariant is proven to respect all known identities of Feynman integrals for graphs. We observe a strong correlation between the tropical and transcendental integrals, which yields a method to approximate unknown Feynman periods.

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“…E y/ D E y E v T is linear. Together with the well-known log-concavity of matroid polynomials [1,87], it can be shown that the function . E y/ is also log-concave within each tree sector.…”

Section: Proof Contraction and Deletion Of An Edge Show Thatmentioning

confidence: 98%