@article {IOPORT.06045673,
    author       = {Cori, Robert and Mathieu, Claire and Robson, John Michael},
    title        = {On the number of indecomposable permutations with a given number of cycles.},
    year         = {2012},
    journal      = {The Electronic Journal of Combinatorics [electronic only]},
    volume       = {19},
    number       = {1},
    issn         = {1077-8926},
    pages        = {Research Paper P49, 14 p., electronic only},
    publisher    = {Prof. Andr\'e K\"undgen, Deptartment of Mathematics, California State University San Marcos, San Marcos, CA},
    abstract     = {Summary: A permutation $a_1a_2\ldots a_n$ is indecomposable if there does not exist $p<n$ such that $a_1a_2\ldots a_p$ is a permutation of $\{ 1,2,\ldots,p\}$. We consider the probability that a permutation of ${\Bbb S}_n$ with $m$ cycles is indecomposable and prove that this probability is monotone non-increasing in $n$.We compute also the asymptotic probability when $n$ goes to infinity with $m/n$ tending to a fixed ratio. The asymptotic probability is monotone in $m/n$, and there is no threshold phenomenon: it degrades gracefully from 1 to 0. When $n=2m$, a slight majority ($51.117\ldots$ percent) of the permutations are indecomposable.},
    identifier   = {06045673},
}