On a Bound in Extremal Combinatorics

A. M. Raigorodskii^a^,^b^,^c^,* and A. A. Sagdeev^a^,^b^,**
Translated by O. Sipacheva

^aMoscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow oblast, 141700 Russia

^bMechanics and Mathematics Faculty, Moscow State University, Moscow, 119991 Russia

^cInstitute of Mathematics and Computer Science, Buryat State University, Ulan-Ude, 670000 Buryat Republic, Russia

Correspondence to: *e-mail: mraigor@yandex.ru
Correspondence to: **e-mail: xp1@protonmail.com

Received 25 August, 2017

Abstract—A new statement of a recent theorem of [1, 2] on the maximum number of edges in a hypergraph with forbidden cardinalities of edge intersections is given. This statement is fundamentally simpler than the original one, which makes it possible to obtain important corollaries in combinatorial geometry and Ramsey theory.

DOI: 10.1134/S1064562418010155