Asymptotic Behaviour of the Castelnuovo-Mumford Regularity

In this paper the asymptotic behavior of the Castelnuovo$ndash;Mumford regularity of powers of a homogeneous ideal I is studied. It is shown that there is a linear bound for the regularity of the powers I whose slope is the maximum degree of a homogeneous generator of I, and that the regularity of I is a linear function for large n. Similar results hold for the integral closures of the powers of I. On the other hand we give examples of ideal for which the regularity of the saturated powers is asymptotically not a linear function, not even a linear function with periodic coefficients.     

Freiman ideals

In this paper we study the Freiman inequality for the least number of generators of the square of an equigenerated monomial ideal. Such an ideal is called a Freiman ideal if equality holds in the Freiman inequality. We classify all Freiman ideals of maximal height, the Freiman ideals of certain classes of principal Borel ideals, the Hibi ideals which are Freiman, and classes of Veronese type ideals which are Freiman.     

因子中原子CSL代数的Lie理想

设B是带有Cartan子代数D的因子,T(L)是B中的原子CLS代数．本文讨论了T(L)中的Lie理想的结构．证明了T(L)中的σ-弱闭子空间L是T(L)的一个Lie理想当且仅当存在T(L)的一个σ-弱闭的结合理想J和T(L)的对角部分的中心的一个子空间E使得(J)~0■L■J E,其中J~0是J中迹为0的元的全体．     

An Upper Bound for the Regularity of Ideals of Borel Type

We show that the regularity of monomial ideals of K[x ₁,…, x _n ] (K being a field), whose associated prime ideals are totally ordered by inclusion is upper bounded by a linear function in n.     

Squarefree Vertex Cover Algebras

In this paper we introduce squarefree vertex cover algebras and exhibit a duality for them. We study the question when these algebras are standard graded and when these algebras coincide with the ordinary vertex cover algebras. It is shown that this is the case for simplicial complexes corresponding to principal Borel sets. Moreover, the generators of these algebras are explicitly described.     

Stability of associated primes of integral closures of monomial ideals

Let I be a monomial ideal of a polynomial ring R=K[X₁,…,Xr] and d(I) the maximal degree of minimal generators of I. In this paper, we explicitly determine a number n₀ in terms of r and d(I) such that for all n?n₀. Furthermore, our n₀ is almost sharp.     

The Lefschetz Property for Componentwise Linear Ideals and Gotzmann Ideals

Abstract

For standard graded Artinian K-algebras defined by componentwise linear ideals and Gotzmann ideals, we give conditions for the weak Lefschetz property in terms of numerical invariants of the defining ideals.     

容斥原理在汉密尔顿问题中的应用

容斥原理是组合数学中的经典的计数方法,该原理的基本思想是:先不排除重叠的情况,把包含于某种性质的所有对象的数目先计算出来,然后再把重复计算的数目排斥出去.针对汉密尔顿问题,[15]利用邻接矩阵给出了判断一个图是否为汉密尔顿图的充要条件.本文将结合容斥原理给出汉密尔顿路径存在性的一个判别条件,并给出汉密尔顿路径的计算公式.     

Maximally differential ideals in regular local rings

It is shown that ifA is a regular local ring andI is a maximally differential ideal inA, thenI is generated by anA-sequence.     

闭模糊n级正关联理想

引入闭模糊n级正关联理想 ,刻划其结构和性质。     

The Integral Closure of Ideals in ℂ{x,y}

Abstract

We give some techniques to determine the ideal K _I generated by the monomials x ^{k ₁} y ^{k ₂} belonging to the integral closure ī of an ideal I ? ?{x, y}. We also give a sufficient condition for a weighted homogeneous ideal I ? ?{x, y} to satisfy the relation ī = I + K _I .