Enumeration of Steiner triple systems with subsystems

A Steiner triple system of order υ, an STS(v), is a set of 3-element subsets, called blocks, of a v-element set of points, such that every pair of distinct points occurs in exactly one block. A subsystem of order w in an STS(v), a sub-STS(w), is a subset of blocks that forms an STS(w). Constructive...

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Bibliographic Details
Published in:Mathematics of computation 2015-11, Vol.84 (296), p.3051-3067
Main Authors: KASKI, PETTERI, ÖSTERGÅRD, PATRIC R. J., POPA, ALEXANDRU
Format: Article
Language:English
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Summary:A Steiner triple system of order υ, an STS(v), is a set of 3-element subsets, called blocks, of a v-element set of points, such that every pair of distinct points occurs in exactly one block. A subsystem of order w in an STS(v), a sub-STS(w), is a subset of blocks that forms an STS(w). Constructive and nonconstructive techniques for enumerating up to isomorphism the STS(v) that admit at least one sub-STS(w) are presented here for general parameters v and w. The techniques are further applied to show that the number of isomorphism classes of STS(21)s with at least one sub-STS(9) is 12661527336 and of STS(27)s with a sub-STS(13) is 1356574942538935943268083236.
ISSN:0025-5718
1088-6842
DOI:10.1090/mcom/2945