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

  • Koganov L
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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 λ are mutually deducible from one another when λ = 2k.
The necessary bijections differ for even and odd values of n.

Author-supplied keywords

  • Chromatic polynomial of a graph
  • Cyclically irreducible word
  • Proper word
  • Whitney formula for the chromatic polynomial of a simple cycle

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Authors

  • Lenya M. Koganov

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