# 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 F of subsequences increasing both in number and in length
at the same time. Let ^{j}F be the set of subsequences of the form
^{j}σ(j+1)(j+2), σ being any permutation on
{1,...,j}.
For j=1 the only subsequence in F is ^{1}123 and the
123-avoiding permutations are enumerated by the Catalan numbers; for
j=2 the subsequences in F are ^{2}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 F are ^{j}j! and their length is (j+2) the
permutations avoiding these j! subsequences are enumerated by a number
sequence
{a such that _{n}}C, _{n} ≤ a_{n} ≤ n!C being
the _{n}nth Catalan number.
For each j we determine the generating function of permutations
avoiding the subsequences in F according to the length, to the number
of left minima and of non-inversions.
^{j}If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |

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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