Results 1 to 10 of about 237,348 (199)

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]

Adv Intell Discov
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
europepmc   +2 more sources

Hadamard Product of Monomial Ideals and the Hadamard Package

Mathematics
In this paper, we generalize and study the concept of Hadamard product of ideals of projective varieties to the case of monomial ideals. We have a research direction similar to the one of the join of monomial ideals contained in a paper of Sturmfels and ...
Guardo Elena
exaly   +3 more sources

Some counterexamples for (strong) persistence property and (nearly) normally torsion-freeness

Examples and Counterexamples, 2023
In this article, we present some rare counterexamples, which are related to (strong) persistence property and (nearly) normally torsion-freeness of monomial ideals.
Mehrdad Nasernejad
doaj   +1 more source

Monomial s-sequences arising from graph ideals

Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2023
Ideals arising from graphs are investigated via s-sequence theory. In particular, the notion of s-sequence for the generators of the edge ideal I(G) of an acyclic graph G is considered for describing the Groebner basis of the relation ideal J of the ...
Maurizio Imbesi, Monica La Barbiera
doaj   +1 more source

Monomial Curves in Afinne Space and their Associated Prime Ideals with Six Generators as Set-Theoretic Complete Intersections

Communications, 2014
The paper deals with the problem of the expression of associated prime ideals of monomial curves in the affine space A4 as set-theoretic complete intersections.
Michaela Holesova
doaj   +1 more source

Steiner Configurations Ideals: Containment and Colouring

Mathematics, 2021
Given a homogeneous ideal I⊆k[x0,…,xn], the Containment problem studies the relation between symbolic and regular powers of I, that is, it asks for which pairs m,r∈N, I(m)⊆Ir holds.
Edoardo Ballico, Giuseppe Favacchio, Elena Guardo, Lorenzo Milazzo, Abu Chackalamannil Thomas   +4 more
doaj   +1 more source

On the Stanley Depth of Powers of Monomial Ideals

Mathematics, 2019
In 1982, Stanley predicted a combinatorial upper bound for the depth of any finitely generated multigraded module over a polynomial ring. The predicted invariant is now called the Stanley depth. Duval et al.
S. A. Seyed Fakhari
doaj   +1 more source

Bar Code and Janet-like division

Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2022
Bar Codes are combinatorial objects encoding many properties of monomial ideals. In this paper we employ these objects to study Janet-like divisions.
Michela Ceria
doaj   +1 more source

Study and characterization of some classes of polymatroidal ideals

پژوهش‌های ریاضی, 2022
Introduction Throughout this paper, we consider monomial ideals of the polynomial ring  over a filed. We try to give some properties of the polymatroidal ideals, which are the special class of monomial ideals.
Somayeh Bandari
doaj  

Ideals with linear quotients in Segre products [PDF]

Opuscula Mathematica, 2017
We establish that the Segre product between a polynomial ring on a field \(K\) in \(m\) variables and the second squarefree Veronese subalgebra of a polynomial ring on \(K\) in \(n\) variables has the intersection degree equal to three.
Gioia Failla
doaj   +1 more source