On the Erd\H{o}s-Purdy problem and the Zarankiewitz problem for semialgebraic graphs

Autor:	Frankl, Nora, Kupavskii, Andrey
Rok vydání:	2021
Předmět:	Mathematics - Combinatorics Computer Science - Discrete Mathematics
Druh dokumentu:	Working Paper
Popis:	Erd\H{o}s and Purdy, and later Agarwal and Sharir, conjectured that any set of $n$ points in $\mathbb R^{d}$ determine at most $Cn^{d/2}$ congruent $k$-simplices for even $d$. We obtain the first significant progress towards this conjecture, showing that this number is at most $C n^{3d/4}$ for $k
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2112.10245 Zobrazit plný text záznamu View this record from Arxiv