Combinatorics of geometrically distributed random variables: left-to-right maxima
FPSAC '93 Proceedings of the 5th conference on Formal power series and algebraic combinatorics
A generating function approach to random subgraphs of the n-cycle
Discrete Mathematics
Average Case Analysis of Algorithms on Sequences
Average Case Analysis of Algorithms on Sequences
Distinctness of compositions of an integer: a probabilistic analysis
Random Structures & Algorithms - Special issue on analysis of algorithms dedicated to Don Knuth on the occasion of his (100)8th birthday
Analytic Combinatorics
Asymptotic behavior of permutation records
Journal of Combinatorial Theory Series A
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A composition@s=a"1a"2...a"m of n is an ordered collection of positive integers whose sum is n. An element a"i in @s is a strong (weak) record if a"ia"j (a"i=a"j) for all j=1,2,...,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,...,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.