Independent sets of closure operations

Enumerating maximal consistent closed sets in closure systems

Given an implicational base, a well-known representation for a closure system, an inconsistency binary relation over a finite set, we are interested in the problem of enumerating all maximal consistent closed sets (denoted by MCCEnum for short). We show that MCCEnum cannot be solved in output-polynomial time unless $\textsf{P} = \textsf{NP}$, even for lower bounded lattices. We give an incremental-polynomial time algorithm to solve MCCEnum for closure systems with constant Carathéodory number. Finally we prove that in biatomic atomistic closure systems MCCEnum can be solved in output-quasipoly…

Well quasi-orders and the shuffle closure of finite sets

Given a set I of word, the set of all words obtained by the shuffle of (copies of) words of I is naturally provided with a partial order. In [FS05], the authors have opened the problem of the characterization of the finite sets I such that the order is a well quasi-order . In this paper we give an answer in the case when I consists of a single word w.

Ramsey Classes with Closure Operations (Selected Combinatorial Applications)

We state the Ramsey property of classes of ordered structures with closures and given local properties. This generalises many old and new results: the Nešetřil-Rödl Theorem, the author's Ramsey lift of bowtie-free graphs as well as the Ramsey Theorem for Finite Models (i.e. structures with both functions and relations) thus providing the ultimate generalisation of Structural Ramsey Theorem. We give here a more concise reformulation of recent authors paper "All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms)" and the main purpose of this paper is to show several …

可由UTVPI表示的整数点集：离散凸性、多态性与成对闭包

UTVPI-representable integer point sets: discrete convexity, polymorphisms, and pairwise closure

该研究关联整数点集的不等式表示、离散凸性等五个视角，完全刻画了UTVPI可表示性，建立成对闭包理论并确定相关类的包含层次。

闭包运算产生解的高效枚举

Efficient enumeration of solutions produced by closure operations

本文提出用多项式延迟枚举布尔关系在自同态下的闭包，并证明相应成员问题在布尔情形属P类，在更大定义域上对某些运算为NP难，同时将闭包极值生成与拟阵回路和超图极大独立集枚举等经典问题关联。

The Triangle Closure is a Polyhedron

Recently, cutting planes derived from maximal lattice-free convex sets have been studied intensively by the integer programming community. An important question in this research area has been to decide whether the closures associated with certain families of lattice-free sets are polyhedra. For a long time, the only result known was the celebrated theorem of Cook, Kannan and Schrijver who showed that the split closure is a polyhedron. Although some fairly general results were obtained by Andersen, Louveaux and Weismantel [ An analysis of mixed integer linear sets based on lattice point free co…