A combinatorial approach to colourful simplicial depth
Antoine Deza

17 October 2013, 14:00 - 17 October 2013, 15:00 Salle/Bat : 475/PCRI-N
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Résumé :

A combinatorial approach to colourful simplicial depth
Antoine Deza, McMaster university, Hamilton, Ontario, Canada

The colourful simplicial depth conjecture states that any point in
the convex hull of each of d+1 sets, or colours, of d+1 points in
general position in dimension d is contained in at least d^2+1
simplices with one vertex from each set. We verify the conjecture in
dimension 4 and strengthen the known lower bounds in higher
dimensions. These results are obtained using a combinatorial
generalization of colourful point configurations called octahedral
systems. We present properties of octahedral systems generalizing
earlier results on colourful point configurations and exhibit an
octahedral system which cannot arise from a colourful point
configuration. The number of octahedral systems is also given.

based on joint-work with Frédéric Meunier (Université Paris Est,
CERMICS) and Pauline Sarrabezolles (Université Paris Est, CERMICS)