论文信息 - A Permutation on Words in a Two Letter Alphabet

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.

[1] T. Motzkin,et al. A problem of arrangements , 1947 .

[2] E. Guitter,et al. Meanders: A direct enumeration approach , 1996, hep-th/9607039.

[3] M. Lothaire,et al. Algebraic Combinatorics on Words: Index of Notation , 2002 .

[4] Roland Speicher,et al. The Non-Commutative Cycle Lemma , 2009, J. Comb. Theory, Ser. A.

[5] T. Storer. Cyclotomy and difference sets , 1967 .

[6] Robert Cori,et al. Some permutations on Dyck words , 2016, Theor. Comput. Sci..

[7] L. D. Baumert. Cyclic Difference Sets , 1971 .

[8] M. Lothaire. Algebraic Combinatorics on Words , 2002 .

[9] Jacques Touchard. Contribution à l'étude du problème des timbres poste , 1950 .

[10] Robert Cori,et al. COUNTING GENUS ONE PARTITIONS AND PERMUTATIONS , 2013, 1306.4628.

[11] Stéphane Legendre,et al. Foldings and meanders , 2013, Australas. J Comb..

[12] A. K. Zvonkin,et al. Plane and Projective Meanders , 1993, Theor. Comput. Sci..

[13] Robert Cori,et al. Une Preuve Combinatiore de la Rationalité d'une Série Génératrice Associée aux Arbres , 1982, RAIRO - Theoretical Informatics and Applications.