Discrete Mathematics & Theoretical Computer Science
Volume 4 n° 1 (2000), pp. 31-44
| author: | Elena Barcucci and Alberto Del Lungo and Elisa Pergola and Renzo Pinzani |
|---|---|
| title: | Permutations avoiding an increasing number of length-increasing forbidden subsequences |
| keywords: | Permutations, Forbidden subsequences, Catalan numbers, Schröder numbers |
| abstract: | A permutation π is said to be τ-avoiding if it does not contain any subsequence having all the same pairwise comparisons as
τ.
This paper concerns the characterization and enumeration of permutations which
avoid a set Fj of subsequences increasing both in number and in length
at the same time. Let Fj be the set of subsequences of the form
σ(j+1)(j+2), σ being any permutation on
{1,...,j}.
For j=1 the only subsequence in F1 is 123 and the
123-avoiding permutations are enumerated by the Catalan numbers; for
j=2 the subsequences in F2 are 1234 2134 and the
(1234,2134)avoiding permutations are enumerated by the Schröder
numbers; for each other value of j greater than 2 the
subsequences in Fj are j! and their length is (j+2) the
permutations avoiding these j! subsequences are enumerated by a number
sequence
{an} such that Cn ≤ an ≤ n!, Cn being
the nth Catalan number.
For each j we determine the generating function of permutations
avoiding the subsequences in Fj according to the length, to the number
of left minima and of non-inversions.
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| reference: | Elena Barcucci and Alberto Del Lungo and Elisa Pergola and Renzo Pinzani (2000), Permutations avoiding an increasing number of length-increasing forbidden subsequences , Discrete Mathematics and Theoretical Computer Science 4, pp. 31-44 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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