Mardi 16 Septembre


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Mardi 16 Septembre
Heure: 12:00 - 13:00
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: Lexicographical polytopes
Description: Michele Barbato Within a fixed integer box of R^n, the lexicographical polytopes are the convex hulls of the integer points that are lexicographically between two given integer points. We prove that, together with the bounds, the linear inequalities that arise naturally when characterizing those points suffice to describe these polytopes. As a consequence, this family of integer polytopes is closed by intersection.
Beside, we prove that lexicographical polytopes are precisely the superincreasing knapsacks described by Gupte. Our contribution is to provide significantly simpler and shorter proofs.
This is a joint work with Roland Grappe, Mathieu Lacroix and Clément Pira.