Geodesic
Counting stabilized-interval-free permutations
Journal of integer sequences, Tome 7 (2004) no. 1
A stabilized-interval-free (SIF) permutation on $[n] = { 1,2,\dots ,n }$ is one that does not stabilize any proper subinterval of $[n]$. By presenting a decomposition of an arbitrary permutation into a list of SIF permutations, we show that the generating function $A(x)$ for SIF permutations satisfies the defining property: [x^n-1] $A(x)^n = n$! . We also give an efficient recurrence for counting SIF permutations.
Classification : 05A05, 05A15
Keywords: stabilized-interval-free, connected, indecomposable, noncrossing partition, murasaki diagram, Dyck path 
@article{JIS_2004__7_1_a0,
     author = {Callan,  David},
     title = {Counting stabilized-interval-free permutations},
     journal = {Journal of integer sequences},
     year = {2004},
     volume = {7},
     number = {1},
     zbl = {1065.05006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2004__7_1_a0/}
}
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Callan,  David. Counting stabilized-interval-free permutations. Journal of integer sequences, Tome 7 (2004) no. 1. http://geodesic.mathdoc.fr/item/JIS_2004__7_1_a0/