اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدComputing the degree of a lattice ideal of dimension one
101
0
0.0
(
0
)
نشر من قبل
Rafael Villarreal H
تاريخ النشر
2012
مجال البحث
الهندسة المعلوماتية
والبحث باللغة
English
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We show that the degree of a graded lattice ideal of dimension 1 is the order of the torsion subgroup of the quotient group of the lattice. This gives an efficient method to compute the degree of this type of lattice ideals.
قيم البحث
اقرأ أيضاً
In this paper we develop a new technique to compute the Betti table of a monomial ideal. We present a prototype implementation of the resulting algorithm and we perform numerical experiments suggesting a very promising efficiency. On the way of descr
ibing the method, we also prove new constraints on the shape of the possible Betti tables of a monomial ideal.
Let $G$ be a connected graph and let $mathbb{X}$ be the set of projective points defined by the column vectors of the incidence matrix of $G$ over a field $K$ of any characteristic. We determine the generalized Hamming weights of the Reed--Muller-typ
e code over the set $mathbb{X}$ in terms of graph theoretic invariants. As an application to coding theory we show that if $G$ is non-bipartite and $K$ is a finite field of ${rm char}(K) eq 2$, then the $r$-th generalized Hamming weight of the linear code generated by the rows of the incidence matrix of $G$ is the $r$-th weak edge biparticity of $G$. If ${rm char}(K)=2$ or $G$ is bipartite, we prove that the $r$-th generalized Hamming weight of that code is the $r$-th edge connectivity of $G$.
We compute the basic parameters (dimension, length, minimum distance) of affine evaluation codes defined on a cartesian product of finite sets. Given a sequence of positive integers, we construct an evaluation code, over a degenerate torus, with pres
cribed parameters. As an application of our results, we recover the formulas for the minimum distance of various families of evaluation codes.
In this paper we provide some precise formulas for regularity of powers of edge ideal of the disjoint union of some weighted oriented gap-free bipartite graphs. For the projective dimension of such an edge ideal, we give its exact formula. Meanwhile,
we also give the upper and lower bounds of projective dimension of higher power of such edge ideals. Some examples show that these formulas are related to direction selection.
We introduce the combinatorial Lyubeznik resolution of monomial ideals. We prove that this resolution is isomorphic to the usual Lyubezbnik resolution. As an application, we give a combinatorial method to determine if an ideal is a Lyubeznik ideal. F
urthermore, the minimality of the Lyubeznik resolution is characterized and we classify all the Lyubeznik symbols using combinatorial criteria. We get a combinatorial expression for the projective dimension, the length of Lyubeznik, and the arithmetical rank of a monomial ideal. We define the Lyubeznik totally ideals as those ideals that yield a minimal free resolution under any total order. Finally, we present that for a family of graphics, that their edge ideals are Lyubeznik totally ideals.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
