A Permutation on Words in a Two Letter Alphabet
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.
- 10.Lothaire, M.: Combinatorics on words. In: Encyclopedia of Mathematics and its Applications, vol. 17. Addison-Wesley Publishing Co., Reading (1983)Google Scholar
- 11.Lothaire, M.: Algebraic combinatorics on words. In: Encyclopedia of Mathematics and its Applications, vol. 90. Cambridge University Press, Cambridge (2002)Google Scholar
- 12.Storer, T.: Cyclotomy and difference sets. In: Lectures in Advanced Mathematics, no. 2. Markham Publishing Co., Chicago (1967)Google Scholar