Mathématiques et sciences humaines. Mathematics and social sciences | |
Le cône des représentations d’un ordre d’intervalles | |
Doignon, Jean-Paul1  Pauwels, Christophe1  | |
关键词: convex polyhedron; interval order; interval ordre representation; | |
DOI : 10.4000/msh.12061 | |
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 】
A fixed, interval order is considered on a finite set of elements. When appropriately defined, its representations form a convex polyhedron. Our results describe the geometricstructure of the polyhedron. The facets are in a one-to-one correspondence with the objects of oneof four types: the minimal elements, the contractible elements as well as the noses and the hollowsof the interval order (the latter notions are inferred from Doignon and Falmagne [1997]). Thepolyhedron has only one vertex, which is the minimal representation (in the meaning of Doignon[1988a]; new properties are established here). All representations thus form a convex cone. Wecharacterize the extreme rays of this cone. The uniqueness of the vertex came as a surprise tous surprise because Balof, Doignon and Fiorini [2012] obtained, for the polyhedron formed by allrepresentations of a semiorder, numerous examples with multiple vertices.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912020428867ZK.pdf | 537KB | download |