Geodesic
Permutations avoiding an increasing number of length-increasing forbidden subsequences
Discrete mathematics & theoretical computer science, Tome 4 (2000-2001) no. 1.

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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^j of subsequences increasing both in number and in length at the same time. Let F^j 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 F^1 is 123 and the 123-avoiding permutations are enumerated by the Catalan numbers; for j=2 the subsequences in F^2 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 F^j are j! and their length is (j+2) the permutations avoiding these j! subsequences are enumerated by a number sequence \a_n\ such that C_n ≤ a_n ≤ n!, C_n being the nth Catalan number. For each j we determine the generating function of permutations avoiding the subsequences in F^j according to the length, to the number of left minima and of non-inversions. 
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     author = {Barcucci, Elena and Del Lungo, Alberto and Pergola, Elisa and Pinzani, Renzo},
     title = {Permutations avoiding an increasing number of length-increasing forbidden subsequences},
     journal = {Discrete mathematics & theoretical computer science},
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     year = {2000-2001},
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Barcucci, Elena; Del Lungo, Alberto; Pergola, Elisa; Pinzani, Renzo. Permutations avoiding an increasing number of length-increasing forbidden subsequences. Discrete mathematics & theoretical computer science, Tome 4 (2000-2001) no. 1. doi : 10.46298/dmtcs.273. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.273/

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