A Permutation on Words in a Two Letter Alphabet
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We define a permutation \(\varGamma _n\) on the set of words with n occurrences of the letter a and \(n+1\) occurrences of the letter b. The definition of this permutation is based on a factorization of these words that allows to associate a non crossing partition to them. We prove that all the cycles of this permutation are of odd lengths. We will prove also other properties of this permutation \(\varGamma _n\), one of them allows to build a family of strips of stamps.
KeywordsDyck words Permutations Strips of stamps
We are very grateful for the many valuable comments of the reviewers which improved the article presentation.
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