A combinatorial proof of a result for permutation pairs

Toufik Mansour, Mark Shattuck

Research output: Contribution to journalArticlepeer-review


In this paper, a direct combinatorial proof is given of a result on permutation pairs originally due to Carlitz, Scoville, and Vaughan and later extended. It concerns showing that the series expansion of the reciprocal of a certain multiply exponential generating function has positive integer coefficients. The arguments may then be applied to related problems, one of which concerns the reciprocal of the exponential series for Fibonacci numbers.

Original languageEnglish
Pages (from-to)797-806
Number of pages10
JournalCentral European Journal of Mathematics
Issue number2
StatePublished - Apr 2012


  • Combinatorial proof
  • Exponential generating function
  • Permutations

ASJC Scopus subject areas

  • General Mathematics


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