Asymptotic evaluation of the sat-function for \(r\)-stars
type: Item
instance of: scholarly article
title: Asymptotic evaluation of the sat-function for \(r\)-stars
zbMATH Open document ID: 0949.05045
DOI: 10.1016/S0012-365X(99)00309-X
author: Oleg Pikhurko
published in: Discrete Mathematics
publication date: 2000-03-23T00:00:00Z
review text: Let \(S^r_m\) be the \(r\)-uniform set system on \(m\) vertices consisting of all \(r\)-tuples containing a given vertex. The author proves the following result: Let \(m> r\geq 2\) and \(S= S^r_m\). Then \[ {m-r\over 2}\begin{pmatrix} n\\ r-1\end{pmatrix}\geq \text{sat}(n, S)\geq m-\text{sat}(n, S)\geq {m-r\over 2}\begin{pmatrix} n\\ r-1\end{pmatrix}- O(n^{r- 4/3}). \]
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05A16
zbMATH DE Number: 1423750
zbMATH Keywords: asymptotic evaluation
zbMATH Keywords: sat-function
reviewed by: Chunhui Lai
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1423750