Permutations as products of k conjugate involutions

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Let c(°) denote the number of cycles of a permutation ° of n letters, and let Tr(°)=n-c(°). A t-involution is a product of t disjoint transpositions. Let k>2, n>2t. Theorem. ° is the product of k t-involutions if and only if kt =Tr(°)+2r for some nonegative integer r. (For k=2 one more condition is needed; see [2].) As a corollary, the least power of a class of an involution with at least one fixed point that covers the alternating group is determined.

Original languageEnglish
Pages (from-to)240-242
Number of pages3
JournalJournal of Combinatorial Theory. Series A
Issue number2
StatePublished - Sep 1975
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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