3 papers
math.AC2026
Uniformly dominant local rings and Orlov spectra of singularity categories
Ryo Takahashi
We define a uniformly dominant local ring as a commutative noetherian local ring with an integer r such that the residue field is built from any nonzero object in the singularity c…
math.AC2025
Failure of the Lefschetz property for the Graphic Matroid
Ryo Takahashi
We consider the strong Lefschetz property for standard graded Artinian Gorenstein algebras. Such an algebra has a presentation of the quotient algebra of the ring of the differenti…
math.CO2024
Expansions of the Potts model partition function along deletions and contractions
Ryo Takahashi
We establish two expansions of the Potts model partition function of a graph. One is along the deletions of a graph, a rewritten formula given in Biggs (1977). The other is along t…