Maximal arc partitions of designs
type: Item
instance of: scholarly article
title: Maximal arc partitions of designs
zbMATH Open document ID: 1081.51003
author: Jianyong Qiao
author: Sumit K. Garg
published in: Discrete Mathematics
publication date: 2005-06-23T00:00:00Z
review text: An \(\alpha\)-arc in a 2-design is a subset of points that meets every block in either 0 or \(\alpha\) points, and an \(\alpha\)-spread is a collection of \(\alpha\)-arcs that partitions the point set. An \(\alpha\)-arc is called symmetric if the induced design on it is a multiple of a symmetric design, and an \(\alpha\)-spread is called symmetric if all \(\alpha\)-arcs contained in it are symmetric. The authors show that there exists a complementary Hadamard 2-\((\mu m^ 2 -1, {1 \over 2}\mu m^ 2, {1 \over 4}\mu m^ 2)\) design admitting a \({1 \over 2}m\)-spread if and only if there exists an affine 2-\((\mu m^ 2, \mu m, (\mu m -1)/(m-1))\) design and a complementary Hadamard 2-\((m-1, {1 \over 2}m, {1 \over 4}m)\) design.
reviewed by: Norbert Knarr
Mathematics Subject Classification ID: 51E05
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 2182125
zbMATH Keywords: design
zbMATH Keywords: Hadamard 2-design
zbMATH Keywords: affine design
zbMATH Keywords: arc
zbMATH Keywords: spread
MaRDI profile type: Publication
full work available at URL: j.disc.2004.04.031
OpenAlex ID: W1996836212
cites work: Q4718790
cites work: Q5799104
cites work: Q4873725
cites work: Q5184922
cites work: Decompositions of difference sets
cites work: On the line structure of designs
cites work: Maximal arcs in designs
cites work: Maximal arcs and related designs
DOI: 10.1016/J.DISC.2004.04.031
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description: scientific article; zbMATH DE number 2182125