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

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)

A proof of a conjecture of Björner on simplicial polytopes

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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