id: 06030398
dt: j
an: 06030398
au: Knopfmacher, Arnold; Mansour, Toufik
ti: Record statistics in a random composition.
so: Discrete Appl. Math. 160, No. 4-5, 593-603 (2012).
py: 2012
pu: Elsevier Science B.V. (North-Holland), Amsterdam
la: EN
cc: 
ut: composition; record; left-to-right maxima; generating function; Mellin
    transform; asymptotic estimates
ci: 
li: doi:10.1016/j.dam.2011.10.025
ab: Summary: A composition$σ=a_{1}a_{2}\ldots a_{m}$ of $n$ is an ordered
    collection of positive integers whose sum is $n$. An element $a_{i}$ in
    $σ$ is a strong (weak) record if $a_{i}>a_{j} (a_{i}\ge a_{j})$ for
    all $j=1,2,\ldots ,i - 1$. Furthermore, the position of this record is
    $i$. We derive generating functions for the total number of strong
    (weak) records in all compositions of $n$, as well as for the sum of
    the positions of the records in all compositions of $n$, where the
    parts $a_{i}$ belong to $A=[d]:={1,2,\ldots ,d}$ or $A=N$. In
    particular when $A=N$, we find the asymptotic mean values for the
    number, and for the sum of positions of records in compositions of $n$.
rv: