The enumeration of simple permutations.
By Michael Henry Albert, M. Atkinson, Martin Klazar. 2003
100 citations recorded by the source corpus.
A simple permutation is one which maps no proper non-singleton interval onto an interval. We consider the enumeration of simple permutations from several aspects. Our results include a straightforward relationship between the ordinary generating function for simple permutations and that for all permutations, that the coe‐cients of this series are not P-recursive, an asymptotic expansion for these coe‐cients, and a number of congruence results for the coe‐cients of the functional inverse of the ordinary generating function for allpermutations.
Subfields: Algebra and Number Theory, Artificial Intelligence, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/4b0989df89daefb27bde92977cebb5050e170fee
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In Algebra and Number Theory
In Artificial Intelligence
In Discrete Mathematics and Combinatorics
Citations in the corpus
- Permutation classes (2014, background): “Albert, Atkinson, and Klazar [7] gave refined asymptotics for this quantity, showing that it is”
- Congruences for Catalan and Motzkin numbers and related sequences (2004, background): “Albert, Atkinson, and Klazar [1] have studied simple permutations which are those permutations of {1, 2, .”