Geodesic
The component counts of random injections
Dudley Stark1
1Queen Mary, University of London
The electronic journal of combinatorics, Tome 28 (2021) no. 1
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A model of random injections is defined which has domain $A\cup B$ and codomain $A\cup C$, where $A$, $B$ and $C$ are mutually disjoint finite sets such that $|B|\leqslant |C|$. The model encompasses both random permutations, which is the case $B=C=\varnothing$, and random maximum matchings of a complete bipartite graph, which is the case $A=\varnothing$. The possible components of random injections are cycles and paths. Results on the counts of cycles and paths of different sizes are obtained for this model.
DOI : 10.37236/9496
Classification : 05A05, 05C20, 05C30, 05C80, 05C38, 05C12
Mots-clés : random permutations, cycles of a permutation

Dudley Stark  1

1 Queen Mary, University of London 
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Dudley Stark. The component counts of random injections. The electronic journal of combinatorics, Tome 28 (2021) no. 1. doi: 10.37236/9496

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