Direct constructions of large sets of Kirkman triple systems
type: Item
instance of: scholarly article
title: Direct constructions of large sets of Kirkman triple systems
zbMATH Open document ID: 1362.05023
author: Hao Zheng
author: Junling Zhou
author: Yanxun Chang
published in: Designs, Codes and Cryptography
publication date: 2017-03-23T00:00:00Z
review text: The study on the constructions and existence of large sets of Kirkman triple systems can be traced back to 1850, when Cayley and Kirkman independently expounded the solutions for the Kirkman 15 schoolgirls problem. Sylvester further discussed this question for triples systems. Each system can have 455 triples from 15 elements. The problem with large sets of Kirkman triple systems of order 15 was finally solved by \textit{R. H. F. Denniston} [Discrete Math. 9, 229--233 (1974; Zbl 0285.05002)]. During all these decades many questions have been successfully solved, but some questions are open until now. The main purpose of this paper is to study some aspects of relevance and direct constructions of this large sets. For primary definitions refer to the literature in the paper. This paper after reviewing the construction of such structures, aimed at many recursive constructions which will yield several new infinite classes.
reviewed by: Ratnakaram Nava Mohan
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 6696611
zbMATH Keywords: automorphisms
zbMATH Keywords: difference family large sets
zbMATH Keywords: Kirkman School-girl problem
MaRDI profile type: Publication
full work available at URL: s10623-016-0197-4
OpenAlex ID: W2316666092
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DOI: 10.1007/S10623-016-0197-4
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description: scientific article; zbMATH DE number 6696611