Des chaînes et des antichaînes dans les ensembles ordonnés finis

Mathématiques et sciences humaines. Mathematics and social sciences

Caspard, Nathalie¹ 

关键词: antichain;    chain;    Coxeter lattice;    partially ordered set (poset);    Sperner Emanuel;    width;   

DOI  :  10.4000/msh.11716

学科分类：数学（综合）

来源: College de France * Ecole des Hautes Etudes en Sciences Sociales (E H E S S)

【 摘 要 】

One of the numerous fields investigated by Bruno Leclerc is the theory of finite posets. More precisely, he was very interested in properties of posets relative to some particular substructures, the so-called chains and antichains. Many problems in sorting, search and scheduling, that one can find for instance in computer science and operational research, are connected with the computing of the maximum cardinality of an antichain of a poset, that is, of its width.This paper looks into those centers of interest of Bruno’s work, recalling on one hand some strong and classical theorems relating to these notions and, on the other hand, some results by Bruno on these subjects. Our developments only concern the finite case.

【 授权许可】

Unknown