Article
Mathematics, Applied
Takayuki Hibi, Dumitru Stamate
Summary: The non-Gorenstein locus of stable set rings of finite simple perfect graphs is investigated. Combinatorial descriptions are provided for those perfect graphs whose stable set rings are Gorenstein on the punctured spectrum. Additionally, it is shown that, in general, the Cohen-Macaulay type and residue of Cohen-Macaulay graded algebras are largely independent.
COLLECTANEA MATHEMATICA
(2023)
Article
Mathematics
Mitsuhiro Miyazaki
Summary: This paper provides a criterion for the Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph, stating that the ring is Gorenstein if and only if the sizes of maximal cliques are constant and there are no specific types of odd cycles in the graph.
INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA
(2021)
Article
Mathematics
Ela Celikbas, Naoki Endo, Jai Laxmi, Jerzy Weyman
Summary: This article provides a characterization of the almost Gorenstein property of determinantal rings of a symmetric matrix of indeterminates over an infinite field, and gives an explicit formula for ranks of the last two modules in the resolution of determinantal rings using Schur functors.
COMMUNICATIONS IN ALGEBRA
(2022)
Article
Mathematics
Naoki Endo, Shiro Goto, Ryotaro Isobe
Summary: This paper investigates the condition of when fiber products are almost Gorenstein rings as part of the stratification of Cohen-Macaulay rings. It is shown that under certain conditions, the fiber product of Cohen-Macaulay local rings over a regular local ring is almost Gorenstein if and only if the individual rings are also almost Gorenstein. Additionally, other generalizations of Gorenstein properties are explored in the study.
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES
(2021)
Article
Computer Science, Theory & Methods
Christopher de Vries, Masahiko Yoshinaga
Summary: This paper studies the Ehrhart quasi-polynomials of almost integral polytopes and examines the connection between the shape of polytopes and the algebraic properties of the Ehrhart quasi-polynomials.
DISCRETE & COMPUTATIONAL GEOMETRY
(2023)
Article
Mathematics, Applied
Esme Bajo, Matthias Beck
Summary: This paper introduces an alternative approach to understand Ehrhart's theory through the h*-polynomial of the boundary of a polytope, recovering known results about h*-polynomials and their extensions for rational polytopes in a unified manner.
SIAM JOURNAL ON DISCRETE MATHEMATICS
(2023)
Article
Mathematics, Applied
Alessio Moscariello, Francesco Strazzanti
Summary: This paper extends results on almost Gorenstein affine monomial curves to nearly Gorenstein cases, proving that the Cohen-Macaulay type of a nearly Gorenstein monomial curve in A4 is at most 3. It also shows that the elements of the minimal generators of the associated numerical semigroup for a nearly Gorenstein affine monomial curve are relatively coprime.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics
Kenta Mori
Summary: In this paper, we study the algebraic properties (compressedness, Gorensteinness) of the toric rings of perfectly matchable subgraph polytopes, and provide a complete characterization of a graph whose perfectly matchable subgraph polytope is compressed.
GRAPHS AND COMBINATORICS
(2023)
Article
Mathematics, Applied
Giuseppe Zappala
Summary: The study focuses on the resolution properties of almost Gorenstein artinian algebras and provides a new explicit description of the resolution and graded Betti numbers for almost complete intersection ideals of codimension 3. It also characterizes the ideals whose graded Betti numbers can be achieved using artinian monomial ideals.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2022)
Article
Mathematics
Marco D'Anna, Francesco Strazzanti
Summary: The paper introduces the concept of GAS numerical semigroups and almost canonical ideals, which generalize the notions of almost symmetric and 2-AGL numerical semigroups respectively. It also discusses the transfer of the GAS property from a numerical semigroup to its gluing, numerical duplication and dilatation, extending previous results in the field.
COMMUNICATIONS IN ALGEBRA
(2021)
Article
Computer Science, Software Engineering
Yuri Faenza, Gianpaolo Oriolo, Gautier Stauffer
Summary: The paper proposes an algorithmic solution to providing a polynomial-time and computationally attractive separation routine for the stable set polytope of claw-free graphs, avoiding the heavy computational burden of resorting to the ellipsoid method. The separation routine comes with a 'small' extended linear programming formulation and a procedure to derive a linear description of the stable set polytope of claw-free graphs in the original space.
MATHEMATICAL PROGRAMMING
(2021)
Article
Mathematics, Applied
Selvi Kara, Irem Portakal, Akiyoshi Tsuchiya
Summary: This paper investigates lattice polytopes obtained from finite directed graphs, and associates them with Gorenstein toric Fano varieties with terminal singularities. The authors classify all directed graphs that result in toric Fano varieties that are smooth in codimension 2 and Q-factorial in codimension 3.
COLLECTANEA MATHEMATICA
(2023)
Article
Economics
Marina Nunez, Juan Vidal-Puga
Summary: In an information graph situation, a set of agents and a source form a set of nodes in an undirected graph, where adjacent nodes can share information at no cost. We prove that the core of the derived information graph game is a von Neumann-Morgenstern stable set if the information graph is cycle-complete. If the information graph consists of a ring that contains the source, a stable set always exists.
GAMES AND ECONOMIC BEHAVIOR
(2022)
Article
Mathematics, Applied
Zhanping Wang, Ting Mu, Xiaomei Wang
Summary: The text describes the explicit description of Gorenstein injective modules over a triangular matrix ring, as well as constructing a (right) recollement of stable categories of Gorenstein injective modules.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
(2021)
Article
Mathematics
Wolfgang Rump
Summary: This study reveals the equivalence between non-degenerate cycle sets and non-degenerate set-theoretic solutions to the Yang Baxter equation. It shows that retractable primitive cycle sets belong to a small list found previously, while irretractable primitive torsion cycle sets generate a canonical brace with certain properties. The brace has a unique minimal non-zero ideal and a cyclic quotient brace, and the adjoint group of a specific ideal has a trivial center.
JOURNAL OF ALGEBRA
(2022)
