Geodesic
Counting stabilized-interval-free permutations
Journal of integer sequences, Tome 7 (2004) no. 1.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Callan, David},
     title = {Counting stabilized-interval-free permutations},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
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     number = {1},
     year = {2004},
     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/