Enumeration of Steiner triple systems with subsystems
Copyright policy )Enumeration of Steiner triple systems with subsystems
A Steiner triple system of order v v , an STS( v v ), is a set of 3 3 -element subsets, called blocks, of a v v -element set of points, such that every pair of distinct points occurs in exactly one block. A subsystem of order w w in an STS( v v ), a sub-STS( w w ), is a subset of blocks that forms an STS( w w ). Constructive and nonconstructive techniques for enumerating up to isomorphism the STS( v v ) that admit at least one sub-STS( w w ) are presented here for general parameters v v and w w . The techniques are further applied to show that the number of isomorphism classes of STS( 21 21 )s with at least one sub-STS( 9 9 ) is 12661527336 12661527336 and of STS( 27 27 )s with a sub-STS( 13 13 ) is 1356574942538935943268083236 1356574942538935943268083236 .
- Aalto University Finland
- Helsinki Institute for Information Technology Finland
ta113, ta112, Steiner triple system, ta213, Triple systems, ta111, Exact enumeration problems, generating functions, subsystem., enumeration, Steiner systems in finite geometry, classification, ta5141, ta512, subsystem
ta113, ta112, Steiner triple system, ta213, Triple systems, ta111, Exact enumeration problems, generating functions, subsystem., enumeration, Steiner systems in finite geometry, classification, ta5141, ta512, subsystem
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