Latin square determinants II

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Abstract

The theory of latin square determinants may be regarded as a direct continuation of the line of research which led Frobenius to introduce group characters. A previous paper introduced the basic ideas and indicated how the theory relates to quasigroup character theory. The work here sets out further developments. The linear factors of a latin square determinant are characterised. Results on a lower bound for the number of irreducible factors are obtained, and methods to factorise determinants with various kinds of symmetries are given, as well as determinants arising as extensions. A 'Molien series' for a latin square is defined, generalising that arising in group invariant theory. A determinant arising out of a pair of squares is discussed, and when the pair of squares is an orthogonal pair arising from a finite field it is shown that this determinant has a special property. Further examples have been calculated using symbolic manipulation packages.

Original languageEnglish (US)
Pages (from-to)111-130
Number of pages20
JournalDiscrete Mathematics
Volume105
Issue number1-3
DOIs
StatePublished - Aug 14 1992

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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