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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, February 06, 2007, 12:15 pm

**Duration**: This information is not available in the database

**Location**: OAT S15/S16/S17

**Speaker**: Alexander Engström (KTH Stockholm)

The f-vector of a polytope is a list of the number of faces by dimension. The g-theorem states that there is a bijection between the possible f-vectors of d dimensional simplicial polytopes and the M-sequences of length d/2+1. This bijection is a linear transformation and can be defined by a (d/2+1)x(d+1)-matrix which is usually denoted M_d. Björner proved that all 2x2 minors of M_d are nonnegative and derived a comparison theorem for f-vectors of simplicial polytopes. He conjectured that all minors of M_d are nonnegative and I will explain how this can be proved by considering some weighted planar graphs.

Joint work with Michael Björklund.

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