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Predecessors in Random Mappings

Combinatorics, Probability and Computing, 1996
Let ℱnbe the set of random mappings ϕ : {1,…,n} → {1,…,n} (such that every mapping is equally likely). Forxε {l,…,n} the elementsare called the predecessors ofx. LetNrdenote the random variable which counts the number of pointsxε {l,…,n} with exactlyrpredecessors. In this paper we identify the limiting distribution ofNrasn→ ∞.
Gerd Baron, Michael Drmota, Ljuben R. Mutafchiev   +2 more
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Predecessors in a random mapping

Random Structures and Algorithms, 1998
Summary: A random mapping \((T;q)\) of a finite set \(V\), \(V= \{1,2,\dots, n\}\), into itself assigns independently to each \(i\in V\) its unique image \(j\in V\) with probability \(q\) if \(i=j\) and with probability \(P= (1-q)/(n-1)\) if \(i\neq j\). The number of predecessors of elements from a given subset of \(V\) is studied.
openaire   +2 more sources