Higher rank antipodality
Ponente: Márton Naszódi
Institución: Alfréd Rényi Institute of Mathematics y Eötvös Loránd University, Budapest
Tipo de Evento: Investigación
Institución: Alfréd Rényi Institute of Mathematics y Eötvös Loránd University, Budapest
Tipo de Evento: Investigación
| Cuándo |
22/04/2026 de 17:00 a 18:00 |
|---|---|
| Dónde | ZOOM ID 882 9372 3602 |
| Agregar evento al calendario |
vCal
iCal
|
Motivated by general probability theory, we say that a set X in Rd is antipodal of rank k if, for any k+1 elements q1,…,qk+1∈X, there exists an affine map from the convex hull of X to the k-dimensional simplex Δk that maps q1,…,qk+1 onto the k+1 vertices of Δk. For k=1, this coincides with the well-studied notion of (pairwise) antipodality introduced by Klee.
We consider the following natural generalization of Klee’s problem on antipodal sets: what is the maximum size of an antipodal set of rank kin Rd? We present a geometric characterization of antipodal sets of rank k and, adapting the argument of Danzer and Grünbaum originally developed for the case k=1, we prove an upper bound that is exponential in the dimension. We also point out that this problem is connected to a classical question in computer science on finding perfect hash families, which provides a lower bound on the maximum size, also exponential in the dimension.
Joint work with Zsombor Szilágyi and Mihály Weiner.
