56 papers
This paper investigates the Cohen-Macaulayness, purity, and shellability of the -th squarefree powers of edge ideals of whisker graphs by characterizing these properties in terms of the structural features of the underlying graph, such as its girth and bipartiteness, while also computing depths and verifying a related conjecture.
This paper presents a procedure for efficiently computing cohomological support varieties of certain monomial ideals, which leads to the discovery of new examples that are not unions of linear subspaces and a computer-assisted classification of such varieties for homogeneous monomial ideals with six generators over .
This paper establishes a sharp upper bound of $2D_\mathrm{span} + 1\beta_{\mathrm{field}}D_\mathrm{span}$ in both coprime and non-coprime characteristics.
The paper demonstrates that every Hardy field can be extended to an -free Hardy field, a result that connects to classical oscillation criteria and is used to resolve questions posed by Boshernitzan and generalize one of his theorems.
This paper establishes the existence and combinatorial characterization of the asymptotic v-number for Noetherian graded families of homogeneous ideals via Newton-Okounkov regions, while also proving its eventual quasi-linearity and strict inequalities with regularity and multiplicity.
This paper introduces a determinantal method for computing minimal local generalized additive decompositions (GADs) of homogeneous polynomials by minimizing the rank of symbolic inverse systems, proving that this approach guarantees finding all minimal decompositions without tensor extensions whenever the local GAD-rank does not exceed the form's degree.
This paper demonstrates that a lightweight, automated AI pipeline integrating next-generation large language models with citation-based verification can successfully generate and solve sophisticated, research-grade mathematical problems, including previously unpublished questions, with verified results and open-sourced tools.
This paper constructs smooth affine algebras of dimension over an algebraically closed field of characteristic zero that admit nontrivial projective modules of rank with trivial total Chern classes, thereby demonstrating the existence of nontrivial vector bundles whose topological invariants vanish.
This paper investigates the arithmetic of nonzero ideals in multivariate polynomial rings by extending recent factorization techniques to construct new families of atoms and analyzing the specific arithmetic properties and sets of lengths within the submonoid of monomial ideals.
This paper establishes that motivic stable homotopy groups of spheres over an algebraically closed field of characteristic zero are determined by -completed spheres and motivic cohomology, enabling the proof that complex realization induces isomorphisms in specific bidegrees and resolving the conditions under which the universal stably-free module of type admits a free summand.
This paper provides a complete classification of integrally closed domains and finitely generated torsion-free -algebras for which the ring of integer-valued polynomials is a Prüfer domain, proving that in the semiprimitive case, this property holds if and only if is a commutative finite direct product of almost Dedekind domains with finite residue fields satisfying specific boundedness conditions.
This paper constructs examples of noetherian local geometrically normal domains in prime characteristic that are -injective but fail to be -full or -anti-nilpotent, highlighting the critical role of -injectivity's behavior under purely inseparable finite base changes.
This paper characterizes the Cohen-Macaulay property of the square of an edge ideal by constructing the Stanley-Reisner complex of its polarization and applying Reisner's criterion, proving that for several important classes of graphs, is Cohen-Macaulay if and only if is either a pentagon or a single edge.
This paper characterizes graphs whose edge ideals possess Scarf resolutions as exactly the gap-free forests, while also classifying connected graphs where all powers of their edge ideals admit Scarf resolutions and providing recursive constructions for these complexes.
This paper establishes that the rook polynomial of grid polyominoes coincides with the h-polynomial of their corresponding coordinate rings by utilizing simplicial complex theory to generalize previous findings on frame polyominoes.
This paper generalizes a lower bound for the log canonical threshold of -primary ideals to the -threshold in positive characteristic and provides a classification of homogeneous ideals that achieve this minimal singularity threshold, thereby resolving a conjecture by Bivià-Ausina.
This paper provides a characterization of Dedekind domains, including non-Noetherian ones, based on a specific property of their module homomorphisms, utilizing a homological algebra argument in its proof.
Motivated by pseudo-Gorenstein rings, this paper introduces the concept of pseudo-Gorenstein graphs and classifies them within several natural graph families using independence polynomials.
This paper generalizes several topological results and concepts from ring theory to the setting of monoids.
This paper defines contravariantly infinite subcategories of finitely generated modules over a commutative Noetherian ring and establishes several criteria for such infiniteness specifically in the case where the ring is a local complete intersection.