de Matematicas Discrretas
El principal objetivo del Seminario Preguntón es dar a conocer las diferentes líneas de investigación, dentro de las matemáticas discretas, que se trabajan en todo el país (particularmente en Querétaro) como proyectos de tesis doctorales o estancias posdoctorales. En el Seminario Preguntón se propone fomentar el intercambio de ideas y conocimiento para fortalecer los proyectos de todos los participantes.
Organizadoras: Dra. Gabriela Araujo (IM) y Dra. Amanda Montejano (UMDI-FC)
Miercoles 22 de Abril de 2026
17:00 - 18:00 hrs
Higher rank antipodality
Márton Naszódi
Alfréd Rényi Institute of Mathematics and Eötvös Loránd University, Budapest
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 k in 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.