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Number of cyclically irreducible words in the alphabet of a free group of finite rank. (English. Russian original) Zbl 1142.68056
Cybern. Syst. Anal. 43, No. 4, 499-506 (2007); translation from Kibern. Sist. Anal. 2007, No. 4, 39-48 (2007).
Summary: 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 \(\lambda \) are mutually deducible from one another when \(\lambda = 2k\). The necessary bijections differ for even and odd values of \(n\).

68R15 Combinatorics on words
05C15 Coloring of graphs and hypergraphs
20E05 Free nonabelian groups
Full Text: DOI
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