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Cycle Switches in Latin Squares

Wanless, Ian

Description

Cycle switches are the simplest changes which can be used to alter latin squares, and as such have found many applications in the generation of latin squares. They also provide the simplest examples of latin interchanges or trades in latin square designs. In this paper we construct graphs in which the vertices are classes of latin squares. Edges arise from switching cycles to move from one class to another. Such graphs are constructed on sets of isotopy or main classes of latin squares for...[Show more]

dc.contributor.authorWanless, Ian
dc.date.accessioned2015-12-13T23:14:40Z
dc.identifier.issn0911-0119
dc.identifier.urihttp://hdl.handle.net/1885/88725
dc.description.abstractCycle switches are the simplest changes which can be used to alter latin squares, and as such have found many applications in the generation of latin squares. They also provide the simplest examples of latin interchanges or trades in latin square designs. In this paper we construct graphs in which the vertices are classes of latin squares. Edges arise from switching cycles to move from one class to another. Such graphs are constructed on sets of isotopy or main classes of latin squares for orders up to and including eight. Variants considered are when (i) only intercalates may be switched, (ii) any row cycle may be switched and (iii) all cycles may be switched. The structure of these graphs reveals special roles played by N2, pan-Hamiltonian, atomic, semi-symmetric and totally symmetric latin squares. In some of the graphs parity is important because, for example, the odd latin squares may be disconnected from the even latin squares. An application of our results to the compact storage of large catalogues of latin squares is discussed. We also prove lower bounds on the number of cycles in latin squares of both even and odd orders and show these bounds are sharp for infinitely many orders.
dc.publisherSpringer
dc.sourceGraphs and Combinatorics
dc.titleCycle Switches in Latin Squares
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume20
dc.date.issued2004
local.identifier.absfor010104 - Combinatorics and Discrete Mathematics (excl. Physical Combinatorics)
local.identifier.ariespublicationMigratedxPub18521
local.type.statusPublished Version
local.contributor.affiliationWanless, Ian, College of Engineering and Computer Science, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.startpage545
local.bibliographicCitation.lastpage570
local.identifier.doi10.1007/s00373-004-0567-7
dc.date.updated2015-12-12T08:39:49Z
local.identifier.scopusID2-s2.0-11244320527
CollectionsANU Research Publications

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