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- W2798283559 abstract "A $textit{composition}$ $sigma =a_1 a_2 ldots a_m$ of $n$ is an ordered collection of positive integers whose sum is $n$. An element $a_i$ in $sigma$ is a strong (weak) $textit{record}$ if $a_i> a_j (a_i geq a_j)$ 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 fixed subset $A$ of the natural numbers. In particular when $A=mathbb{N}$, we find the asymptotic mean values for the number, and for the sum of positions, of records in compositions of $n$." @default.
- W2798283559 created "2018-05-07" @default.
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- W2798283559 date "2009-01-01" @default.
- W2798283559 modified "2023-09-25" @default.
- W2798283559 title "Record statistics in integer compositions" @default.
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- W2798283559 doi "https://doi.org/10.46298/dmtcs.2691" @default.
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