## Discrete Mathematics & Theoretical Computer Science, Vol 4, No 1 (2000)

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DMTCS vol 4 no 1 (2000), pp. 31-44

# 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 Permutations avoiding an increasing number of length-increasing forbidden subsequences Permutations, Forbidden subsequences, Catalan numbers, Schröder numbers 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. 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. 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 For a corresponding BibTeX entry, please consider our BibTeX-file. dm040103.ps.gz (55 K) dm040103.ps (163 K) dm040103.pdf (142 K)