Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, October 23, 2003, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Yoshio Okamoto

Local topology of the free complex of a two-dimensional generalized convex shelling

How many interior points are there in a given d-dimensional point configuration? For this problem, the Euler-Poincare type formula was given by Ahrens, Gordon & MacMahon when d=2, and they conjecture it holds for higher dimensions. This conjecture was settled independently by Klain and by Edelman & Reiner. The proof by Edelman & Reiner used the topological method and they raised open problems for the further generalization to the so-called "convex geometries" which were first introduced by Edelman & Jamison.

In this work, we consider a subclass of the convex geometries which consists of the 2-dimensional separable generalized convex shelling, and show the conjecture is valid for this class. This is not just a special case but a step toward a resolution of their open problems because it was shown by Kashiwabara, Nakamura & Okamoto that every convex geometry is isomorphic to some d-dimensional separable generalized convex shelling for some d, which we call the representation theorem of convex geometries.

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