Limit behavior of maxima in geometric words representing set partitions

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Limit Behavior of Maxima in Geometric Words representing Set Partitions

We consider geometric words ω1 · · ·ωn with letters satisfying the restricted growth property ωk ≤ d + max{ω0, . . . , ωk−1}, where ω0 := 0 and d ≥ 1. For d = 1 these words are in 1-to-1 correspondence with set partitions and for this case we show that the number of left-to-right maxima (suitable centered) does not converge to a fixed limit law as n tends to infinity. This becomes wrong for d ≥...

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Words satisfying the restricted growth property wk ≤ 1 + max{w0, . . . , wk−1} are in correspondence with set partitions. Underlying the geometric distribution to the letters, these words are enumerated with respect to the largest letter occurring, which corresponds to the number of blocks in the set partition. It turns out that on average, this parameter behaves like log1/q n, where q is the p...

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ژورنال

عنوان ژورنال: Applicable Analysis and Discrete Mathematics

سال: 2015

ISSN: 1452-8630,2406-100X

DOI: 10.2298/aadm150619013f