Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, May 24, 2011, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Arnau Padrol (UPC Barcelona)

Constructing Gale duals of neighborly polytopes

A d-polytope P is neighborly if every subset of at most d/2 vertices is a face of P. In 1982, Shemer introduced a "sewing" construction that allows to add a vertex to a neighborly poltytope obtaining a new neighborly polytope.

Gale duals of neighborly polytopes have a nice geometric characterization: balanced point configurations. A configuration of n points in R^d is balanced if every hyperplane through the origin contains at least floor((n-d+1)/2) points at each of its sides.

We present a construction that allows to add points to a balanced point configuration obtaining a new balanced point configuration. In the dual setting, it constructs a neighborly polytope whose vertex figure at a particular vertex is another prescribed neighborly polytope.

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