Abstract
Let f: ℕ n ∪ {0} → ℤ be a (total) mapping with |f (t) − f (t − 1)| ≤ 1, 0 ≤ t ≤ n. The (n + 1)-tuple ρ f = (f (0), f (1),..., f (n)) is called a random walk of length n from f (0) to f (n). Here, ρ f is said to be simple, if |f (t) − f (t − 1)| = 1, 0 ≤ t ≤ n. The tuple (f (t − 1), f (t)), t ∈ ℕ n , is called the t-th segment of ρ f and is denoted by ρ t f . A segment ρ t f is of type ↑ (type.↓, type ↕), if f (t) > f (t − 1) (f (t) < f (t − 1), f (t) = f (t − 1)). The level of the t-th segment ρ t f , is the value f (t − 1), t ∈ ℕ n .
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© 1984 Springer Fachmedien Wiesbaden
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Kemp, R. (1984). Random Walks, Trees, Lists. In: Fundamentals of the Average Case Analysis of Particular Algorithms. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-12191-6_4
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DOI: https://doi.org/10.1007/978-3-663-12191-6_4
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-519-02100-1
Online ISBN: 978-3-663-12191-6
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