Counting and Generating Permutations Using Timed Languages

  title={Counting and Generating Permutations Using Timed Languages},
  author={Nicolas Basset},
The signature of a permutation σ is a word sg(σ) ⊆ {a,d}∗ whose i letter is d when σ has a descent (i.e. σ(i) > σ(i+ 1)) and is a when σ has an ascent (i.e. σ(i) < σ(i + 1)). Combinatorics of permutations with a prescribed signature is quite well explored. Here we state and address the two problems of counting and randomly generating in the set sg−1(L) of permutations with signature in a given regular language L ⊆ {a,d}∗. First we give an algorithm that computes a closed form formula for the… CONTINUE READING
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