Brändén, Petter and Claesson, Anders and Steingrimsson, Einar (2002) Catalan continued fractions and increasing subsequences in permutations. Discrete Mathematics, 258 (1-3). 275–287. ISSN 0012-365XFull text not available in this repository. (Request a copy from the Strathclyde author)
We call a Stieltjes continued fraction with monic monomial numerators a Catalan continued fraction. Let ek(π) be the number of increasing subsequences of length k+1 in the permutation π. We prove that any Catalan continued fraction is the multivariate generating function of a family of statistics on the 132-avoiding permutations, each consisting of a (possibly infinite) linear combination of the eks. Moreover, there is an invertible linear transformation that translates between linear combinations of eks and the corresponding continued fractions. Some applications are given, one of which relates fountains of coins to 132-avoiding permutations according to number of inversions. Another relates ballot numbers to such permutations according to number of right-to-left maxima.
|Keywords:||Stieltjes continued fraction, Catalan continued fraction, permutations, Electronic computers. Computer science, Discrete Mathematics and Combinatorics, Theoretical Computer Science|
|Subjects:||Science > Mathematics > Electronic computers. Computer science|
|Department:||Faculty of Science > Computer and Information Sciences|
|Depositing user:||Pure Administrator|
|Date Deposited:||14 Oct 2014 15:05|
|Last modified:||22 Mar 2017 13:34|