Runs on a Ring

*To*: mathgroup at smc.vnet.net*Subject*: [mg32312] Runs on a Ring*From*: "Seth Chandler" <SChandler at Central.UH.Edu>*Date*: Sat, 12 Jan 2002 05:18:34 -0500 (EST)*Organization*: University of Houston*Sender*: owner-wri-mathgroup at wolfram.com

This is a combined math and Mathematica problem. Suppose one has a ring of n sites. Each site is populated by a zero or a one, each with random probability one half. What are the odds that in a ring of size n there is at least one run of ones (or, equivalently, zeros) of length t? The problem is solved for lists of site n. See http://mathworld.wolfram.com/Run.html for an excellent discussion, but I have not been able to find a solution for rings. I have been able to solve the problem inelegantly for runs of length 3 by using the package RSolve to solve some coupled difference equations generated largely from observation.