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.


Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks


Automatic MiSe System Software Version 1.4803M   |   admin login