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A Sequential Search Distribution: Proofreading, Russian Roulette, and the Incomplete q-Eulerian Polynomials
Discrete Mathematics and Theoretical Computer Science Proceedings AA (DM-CCG)
  • Travis Herbranson, California Polytechnic State University - San Luis Obispo
  • Don Rawlings, California Polytechnic State University - San Luis Obispo
Publication Date
1-1-2001
Abstract

The distribution for the number of searches needed to find k of n lost objects is expressed in terms of a refinement of the q-Eulerian polynomials, for which formulae are developed involving homogeneous symmetric polynomials. In the case when k = n and the find probability remains constant, relatively simple and efficient formulas are obtained. From our main theorem, we further (1) deduce the inverse absorption distribution and (2) determine the expected number of times the survivor pulls the trigger in an n-player game of Russian roulette.

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Citation Information
Travis Herbranson and Don Rawlings. "A Sequential Search Distribution: Proofreading, Russian Roulette, and the Incomplete q-Eulerian Polynomials" Discrete Mathematics and Theoretical Computer Science Proceedings AA (DM-CCG) (2001) p. 193 - 202
Available at: http://works.bepress.com/drawling/8/