Maximal arcs in designs
type: Item
instance of: scholarly article
title: Maximal arcs in designs
zbMATH Open document ID: 0584.05017
DOI: 10.1007/BF02582933
author: Sharad Sane
author: S. S. Shrikhande
author: N. M. Singhi
published in: Graphs and Combinatorics
publication date: 1985-01-01T00:00:00Z
review text: An (\(\alpha\),n) arc in a design is defined as a nonempty set of n points of the design such that any block intersects this set in at most \(\alpha\) points. An (\(\alpha\),n) arc is said to be maximal if every block meets the arc in either 0 or \(\alpha\) points. A maximal block arc is dually defined. In this paper the infinite family of possibly extendable symmetric designs other than the Hadamard design family and their related designs are studied using maximal arcs. A correspondence between the extendability and the existence of a proper family of maximal arcs as well as a natural duality between point and block arcs are established.
Mathematics Subject Classification ID: 05B30
zbMATH DE Number: 3935056
zbMATH Keywords: point arcs
zbMATH Keywords: design
zbMATH Keywords: extendable symmetric designs
zbMATH Keywords: maximal arcs
zbMATH Keywords: block arcs
reviewed by: S. S. Agayan
MaRDI profile type: Publication
cites work: Ovals in projective designs
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cites work: Extending symmetric designs
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cites work: Q5545191
cites work: On some Theorems in Combinatorics Relating to Incomplete Block Designs
cites work: Classification of (16,6,2)-designs by ovals
cites work: An extension of a theorem of the Bruijn and Erdős on combinatorial designs
cites work: Q3481715
full work available at URL: https://doi.org/10.1007/bf02582933
OpenAlex ID: W2072187058
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description: scientific article; zbMATH DE number 3935056