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Facets of the weak order polytope derived from the induced partition projection

par Doignon, Jean-Paul ;Fiorini, Samuel
Référence SIAM journal on discrete mathematics, 15, page (112-121)
Publication Publié, 2002

Article révisé par les pairs

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Résumé :

The weak order polytopes are studied in Gurgel and Wakabayashi [Discrete Math., 175 (1997), pp. 163-172], Gurgel and Wakabayashi [The Complete Pre-Order Polytope: Facets and Separation Problem, manuscript, 1996], and Fiorini and Fishburn [Weak order polytopes, submitted]. We make use of their natural, affine projection onto the partition polytopes to determine several new families of facets for them. It turns out that not all facets of partition polytopes are lifted into facets of weak order polytopes. We settle the cases of all facet-defining inequalities established for partition polytopes by Grötschel and Wakabayashi [Math. Programming, 47 (1990), pp. 367-387]. Our method, although rather simple, allows us to establish general families of facets which contain two particular cases previously requiring long proofs.