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N.B. A detailed on-line essay by S. Finch was the starting point for this entry.
Let be a
-Vector whose entries are each 1 (with probability
) or 0 (with probability
).
An
-run is an isolated group of
consecutive 1s. Ignoring the boundaries, the total number of runs
satisfies
See also Percolation Theory, s-Cluster
References
Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/rndprc/rndprc.html