Root cases of large sets of \(t\)-designs
type: Item
instance of: scholarly article
title: Root cases of large sets of \(t\)-designs
zbMATH Open document ID: 1013.05013
DOI: 10.1016/S0012-365X(02)00574-5
author: B. Tayfeh-Rezaie
author: Gholamreza Khosrovshahi
published in: Discrete Mathematics
publication date: 2003-04-09T00:00:00Z
review text: A large set of \(t\)-\((v,k,i)\) designs of size \(N\), denoted by LS[N]\((t,k,v)\) is a partition of all \(k\)-subsets of a \(v\)-set into \(N\) disjoint \(t\)-\((v,k,i)\) designs, where \(N = (v-t)!/[(k-t)!(v-k)!i]\). The authors extend some of the recursive methods for constructing large \(t\)-designs of prime sizes, in order to show that, to construct all possible large sets with the given \(N, t, k\), it suffices to construct a finite number of large sets called by the authors root cases. As a corollary, it is shown that the trivial necessary conditions for the existence of LS[3]\((2,k,v)\) are also sufficient for \(k\) equal to or less than \(80\).
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 1896003
zbMATH Keywords: \((N,t)\)-partitionable sets
reviewed by: Mirela Ştefănescu
MaRDI profile type: Publication
full work available at URL: s0012-365x(02)00574-5
OpenAlex ID: W2010614667
description: scientific article; zbMATH DE number 1896003