id: 06098385
dt: j
an: 06098385
au: Homberger, Cheyne
ti: Expected patterns in permutation classes.
so: Electron. J. Comb. 19, No. 3, Research Paper P43, 12 p., electronic only
    (2012).
py: 2012
pu: Prof. André Kündgen, Deptartment of Mathematics, California State
    University San Marcos, San Marcos, CA
la: EN
cc: 
ut: permutations; patterns; Dyck paths
ci: 
li: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i3p43
ab: Summary: Each length $k$ pattern occurs equally often in the set $S_n$ of
    all permutations of length $n$, but the same is not true in general for
    a proper subset of $S_n$. {\it M. Bóna} [Electron. J. Comb. 19, No. 1,
    Research Paper P62, 11 p., electronic only (2012; Zbl 1243.05006)]
    recently proved that if we consider the set of $n$-permutations
    avoiding the pattern 132, all other non-monotone patterns of length 3
    are equally common. In this paper we focus on the set
    $\operatorname{Av}_n (123)$ of $n$-permutations avoiding $123$, and
    give exact formulae for the occurrences of each length 3 pattern. While
    this set does not have the same symmetries as $\operatorname{Av}_n
    (132)$, we find several similarities between the two and prove that the
    number of 231 patterns is the same in each.
rv: