Counting families of mutually intersecting sets
type: Item
instance of: scholarly article
title: Counting families of mutually intersecting sets
zbMATH Open document ID: 1267.05144
author: Yanyan Li
published in: The Electronic Journal of Combinatorics
publication date: 2013-06-07T00:00:00Z
full work available at URL: v20i2p8
review text: Summary: We show that the number of maximal intersecting families on a 9-set equals 423295099074735261880, that the number of independent sets of the Kneser graph \(K(9,4)\) equals \[ 366996244568643864340, \] and that the number of intersecting families on an 8-set and on a 9-set is \[ 14704022144627161780744368338695925293142507520 \] and \[ \begin{multlined} 125532424879405039143639827181122982679752727208\\08010757809032705650591023015520462677475328\end{multlined} \] (roughly \(1.255\cdot 10^{91}\)), respectively.
Mathematics Subject Classification ID: 05C30
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 6171923
zbMATH Keywords: maximal linked systems
zbMATH Keywords: Kneser graph
zbMATH Keywords: counting independent sets
MaRDI profile type: Publication
cites work: On Counting Independent Sets in Sparse Graphs
cites work: Q5638325
cites work: The order dimension of the complete graph
cites work: On Dedekind's Problem: The Number of Monotone Boolean Functions
cites work: Q2957449
cites work: Q4326645
cites work: Q3123684
cites work: Voting fairly: Transitive maximal intersecting families of sets
cites work: Substructure lattices of models of arithmetic
cites work: A computation of the eighth Dedekind number
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description: scientific article; zbMATH DE number 6171923