Number of cyclically irreducible words in the alphabet of a free group of finite rank

  • Authors:

  • L. M. Koganov

  • Affiliations:

  • Scientific Center of Nonlinear Wave Mechanics and Technology, Russian Academy of Science, Moscow, Russia

  • Venue:
  • Cybernetics and Systems Analysis
  • Year:
  • 2007

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Abstract

It is shown that a formula that was independently obtained earlier for the number of cyclically irreducible words of length n in a symmetric alphabet of a finitely generated free group of rank k and the Whitney formula for a chromatic polynomial of a simple nonself-intersecting cycle of length n with a variable 驴 are mutually deducible from one another when 驴 = 2k. The necessary bijections differ for even and odd values of n.