Geodesic
Random orders and gambler's ruin
The electronic journal of combinatorics, Tome 12 (2005)

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Zbl EuDML
We prove a conjecture of Droste and Kuske about the probability that $1$ is minimal in a certain random linear ordering of the set of natural numbers. We also prove generalizations, in two directions, of this conjecture: when we use a biased coin in the random process and when we begin the random process with a specified ordering of a finite initial segment of the natural numbers. Our proofs use a connection between the conjecture and a question about the game of gambler's ruin. We exhibit several different approaches (combinatorial, probabilistic, generating function) to the problem, of course ultimately producing equivalent results.
DOI : 10.37236/1920
Classification : 05A15, 05A19, 60C05
Mots-clés : random linear order 
Andreas Blass; Gábor Braun. Random orders and gambler's ruin. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1920
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     author = {Andreas Blass and G\'abor Braun},
     title = {Random orders and gambler's ruin},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1920},
     zbl = {1075.05004},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1920/}
}
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