The number of permutations with a given number of sequences

Details The number of permutations with a given number of sequences The number of permutations with a given number of sequences

2006-10-15

arxiv.org/abs/math/0610462v1

Mathematics

Combinatorics

5 pages

Scientific paper

P(n,s) denotes the number of permutations of 1,2,...n that have exactly s
sequences. Canfield and Wilf [math.CO/0609704] recently showed that P(n,s) can
be written as a sum of s polynomials in n. We determine these polynomials
explicitly and also obtain explicit expressions for P(n,s) and its fixed-s
generating function u_s(x).

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