Reconstruction of the Neighborhood Deck of an Ordered Set

We show that the neighborhood deck of an ordered set can be reconstructed from the deck of one point deleted subsets. As a consequence of the above results we reconstruct some maximal cards and present short new proofs of the reconstructibility of ordered sets of width 2 and of the recognizability of N-free ordered sets. We also reconstruct the maximal cards of N-free ordered sets.     

Reconstruction of N-free Ordered Sets

We prove that N-free ordered sets are reconstructible.     

On Ordered Sets with Isomorphic Marked Maximal Cards

We prove a necessary condition for two nonisomorphic ordered sets to have two isomorphic marked maximal cards. This condition is used to prove that ordered sets of width 3 with 2 maximal elements are reconstructible and that ordered sets of width 3 are reconstructible if we can reconstruct the marked maximal deck.     

Being a Proper Trapezoid Ordered Set Is a Comparability Invariant

It is proved that if we replace an autonomous subset of a finite proper trapezoid ordered set with a proper trapezoid ordered set, then we obtain a proper trapezoid ordered set provided the autonomous subset is not an antichain, and analogously in the k-dimensional case. As corollaries we obtain that being a proper trapezoid ordered set is a comparability invariant, more generally, proper interval dimension is a comparability invariant.     

偏序集上蕴涵代数的素滤子

偏序集上的蕴涵代数是取值于偏序集上的蕴涵逻辑联结词的一种代数抽象.以偏序集上蕴涵代数中由蕴涵算子引入的逻辑运算t-余范为工具,讨论了偏序集上蕴涵代数的一些性质,然后引入了偏序集上蕴涵代数的素滤子的概念,讨论了素滤子在一定条件下的性质,并给出了一个MP滤子成为素滤子的条件.     

On Pseudocomplemented and Stone Ordered Sets

The aim of this paper is to characterize both the pseudocomplemented and Stone ordered sets in a manner similar to that used previously for Boolean and distributive ordered sets. The sublattice G(A) of the Dedekind–Mac Neille completion DM(A) of an ordered set A generated by A is said to be the characteristic lattice of A. We will show that there are distributive pseudocomplemented ordered sets whose characteristic lattices are not pseudocomplemented. We can define a stronger notion of pseudocomplementedness by demanding that both A and G(A) be pseudocomplemented. It turns out that the two concepts are the same for finite and Stone ordered sets.     

3-连通3-正则图中的可序子集

图G的k元点集X={x1,x2,…,xk}被称为G的k-可序子集,如果X的任意排列都按序排在G的某个圈上.称G是k-可序图,如果G的每一个k元子集都是G的k-可序子集.称G为k-可序Hamilton图,如果X的任意排列都位于G的Hamilton圈上.研究了3-连通3-正则图的可序子集的存在性问题.     

Splittability for Partially Ordered Sets

A topological space X is said to be splittable over a class P of spaces if for every AX there exists continuous f:XYP such that f(A)f(XA) is empty. A class P of topological spaces is said to be a splittability class if the spaces splittable over P are precisely the members of P. We extend the notion of splittability to partially ordered sets and consider splittability over some elementary posets. We identify precisely which subsets of a poset can be split along over an n-point chain. Using these results it is shown that the union of two splittability classes need not be a splittability class and a necessary condition for P to be a splittability class is given.     

Identities in Ordered Sets

The concept of identities in ordered sets is introduced.     

On Pseudocomplemented and Stone Ordered Sets,Addendum

The notion of pseudocomplementedness is weakened in order to obtain a tractable and consistent property of ordered sets, in particular lattices.     

On Equivalence Relations in Ordered Sets

A relationship between equivalence relations in finite ordered sets and linear decompositions is presented.     

Maximal and Minimal Semilattices on Ordered Sets

The map which takes an element of an ordered set to its principal ideal is a natural embedding of that ordered set into its powerset, a semilattice. If attention is restricted to all finite intersections of the principal ideals of the original ordered set, then an embedding into a much smaller semilattice is obtained. In this paper the question is answered of when this construction is, in a certain arrow-theoretic sense, minimal. Specifically, a characterisation is given, in terms of ideals and filters, of those ordered sets which admit a so-called minimal embedding into a semilattice. Similarly, a candidate maximal semilattice on an ordered set can be constructed from the principal filters of its elements. A characterisation of those ordered sets that extend to a maximal semilattice is given. Finally, the notion of a free semilattice on an ordered set is given, and it is shown that the candidate maximal semilattice in the embedding-theoretic sense is the free object.     

On C-left Hyp erideals of Ordered Semihyp ergroups

In this paper, the concept of C-left hyperideals is introduced in ordered semihypergroups, and several related properties are investigated. In particular, we discuss the relationships between the greatest left hyperideals and C-left hyperideals of ordered semihypergroups. Furthermore, we introduce the concept of left bases of an ordered semihypergroup, and give out the sufficient and necessary conditions of the existence of the greatest C-left hyperideal of an ordered semihypergroup by the properties of left bases. The result about C-left ideals in ordered semigroups is generalized to the ordered semihypergroups.     

偏序集最小顶点割算法与最小费用赶工问题

在网络计划问题中,一项大的工程由许多工序合成。工序与工序之间存在着一定的前后关系,每个工序有着自己的正常加工时间和通过赶工所能达到的最短加工时间以及每赶工一天的赶工费用。设一项工程的正常工期为T天,通过对所有可能的工序赶工,整个工程能达到的最短工期为S天。本文的问题是,对于任意给定的t(S t相似文献   

Whaley's Theorem for Finite Lattices

Whaley's Theorem on the existence of large proper sublattices of infinite lattices is extended to ordered sets and finite lattices. As a corollary it is shown that every finite lattice L with |L|≥3 contains a proper sublattice S with |S|≥|L|^1/3. It is also shown that that every finite modular lattice L with |L|≥3 contains a proper sublattice S with |S|≥|L|^1/2, and every finite distributive lattice L with |L|≥4 contains a proper sublattice S with |S|≥3/4|L|. This revised version was published online in June 2006 with corrections to the Cover Date.     

关于定向极小集

本文对定向极小集作了进一步的研究，得到一系列重要性质，文章最后给出连续格为完全分配格的一个充分条件．     

基于偏序集的模糊互补矩阵次序一致性检验与调整

针对模糊互补矩阵次序一致性检验和调整存在争议和繁杂问题,提出了模糊互补矩阵次序一致性检验与调整的偏序集表示方法。在定义了偏序集、模糊互补矩阵、截集矩阵等相关概念基础上,求出模糊互补矩阵B的0.5水平截集矩阵,证明了模糊互补判断矩阵次序一致性和0.5水平截集矩阵为偏序关系矩阵的等价性;模糊互补判断矩阵完全次序一致性的充要条件是任意截集均满足传递性;任意截集满足传递性和偏序关系矩阵的等价性。结果表明,利用0.5水平截集矩阵转换为矩阵来检验模糊互补矩阵的次序一致性;通过调整每个截集矩阵满足传递性并赋值,能够达到模糊互补矩阵完全次序一致性。最后,通过两个算例验证该检验和调整方法的合理性和可行性。     

关于交换序半群的一个注记

给出了正则交换序半群的与素理想结构有关的若干性质，还给出了为有限个主理想的并的交换序半群类中的诺特性，阿基米德性，正则性以及有限生成性之间的一些关系。     

Affine Isomorphism for Partially Ordered Sets

Let A and B be the adjacency matrices of graphs G₁ and G₂ (or the strict zeta matrices of posets P₁ and P₂). Associated with A and B is a particular affine space of matrices, denoted _A,B, such that G₁ is isomorphic to G₂ (resp., P₁ is isomorphic to P₂) if and only if there is a 0-1 matrix in _A,B. Solving this integer programming problem is (notoriously) of unknown complexity, and researchers have considered its relaxation; if there is a nonnegative member of _A,B, then one says that G₁ is fractionally isomorphic to G₂ (resp., P₁ is fractionally isomorphic to P₂.) Several combinatorial characterizations of fractional isomorphism for graphs are known.In this paper we note that fractional isomorphism is not an equivalence relation for posets and introduce a further relaxation by defining P₁ to be affinely isomorphic to P₂ if _A,B is nonempty. (Asking whether _A,B is nonempty is a natural first question preceding the question of whether or not _A,B has a binary member, i.e., whether the graphs or posets are isomorphic.) We prove that affine isomorphism is indeed an equivalence relation on posets and that two posets are affinely ismorphic if and only if the f-vectors of their order complexes are the same. One consequence of this is a proof of an affine version of the Poset Reconstruction Conjecture.