Results 1 to 10 of about 887,096 (204)

Algebraic invariants of the edge ideals of whisker graphs of cubic circulant graphs [PDF]

Heliyon
Let Q be a polynomial ring over a field F and I be an edge ideal associated with the whisker graph of a cubic circulant graph. We discuss the regularity, depth, Stanley depth, and projective dimension of Q/I.
Mujahid Ullah Khan Afridi, Ibad Ur Rehman, Muhammad Ishaq   +2 more
doaj   +2 more sources

Regularity of the edge ideals of perfect [ν,h]-ary trees and some unicyclic graphs [PDF]

Heliyon
We compute the Castelnuovo-Mumford regularity of the quotient rings of edge ideals of perfect [ν,h]-ary trees and some unicyclic graphs.
Fatima Tul Zahra, Muhammad Ishaq, Sarah Aljohani   +2 more
doaj   +2 more sources

Efficient next-generation reservoir computing: An analog in-memory implementation using memristor crossbar arrays [PDF]

iScience
Summary: Reservoir computing has garnered significant attention for its efficiency in processing temporal signals, while the proposed next-generation reservoir computing (NG-RC) further enhances computational efficiency.
Zhuosheng Lin, Xiaona Wu, Zaofeng Chen, Jilong Zhang, Jingliang Deng, Yue Feng   +5 more
doaj   +2 more sources

A non-partitionable Cohen–Macaulay simplicial complex [PDF]

Discrete Mathematics & Theoretical Computer Science, 2020
A long-standing conjecture of Stanley states that every Cohen–Macaulay simplicial complex is partition- able. We disprove the conjecture by constructing an explicit counterexample.
Art M. Duval, Bennet Goeckner, Caroline J. Klivans, Jeremy Martin   +3 more
doaj   +1 more source

Bounds for the minimum distance function

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
Let I be a homogeneous ideal in a polynomial ring S. In this paper, we extend the study of the asymptotic behavior of the minimum distance function δI of I and give bounds for its stabilization point, rI, when I is an F -pure or a square-free monomial ...
Núñez-Betancourt Luis, Pitones Yuriko, Villarreal Rafael H.   +2 more
doaj   +1 more source

POLYMATROIDAL IDEALS AND LINEAR RESOLUTION [PDF]

Journal of Algebraic Systems
Let $S=K[x_1,\ldots,x_n]$ be a polynomial ring over a field $K$ and$I\subset S$ be a monomial ideal with a linearresolution. Let$\frak{m}=(x_1,\ldots,x_n)$ be the unique homogeneous maximal ideal and $I\frak{m}$ be apolymatroidal ideal.
Somayeh Bandari
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

On hereditary irreducibility of some monomial matrices over local rings

Karpatsʹkì Matematičnì Publìkacìï, 2021
We consider monomial matrices over a commutative local principal ideal ring $R$ of type $M(t,k,n)=\Phi\left(\begin{smallmatrix}I_k&0\\0\,\,&tI_{n-k}\end{smallmatrix}\right ...
A.A. Tylyshchak, M. Demko
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  

Free Resolutions and Generalized Hamming Weights of Binary Linear Codes

Mathematics, 2022
In this work, we explore the relationship between the graded free resolution of some monomial ideals and the Generalized Hamming Weights (GHWs) of binary codes.
Ignacio García-Marco, Irene Márquez-Corbella, Edgar Martínez-Moro, Yuriko Pitones   +3 more
doaj   +1 more source