A Sequential Search Distribution: Proofreading, Russian Roulette, and the Incomplete q-Eulerian Polynomials

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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Cori, Robert and Mazoyer, Jacques and Morvan, Michel and Mosseri, Rémy. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001), pp.193-202, 2001, DMTCS Proceedings
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Travis Herbranson, Don Rawlings. A Sequential Search Distribution: Proofreading, Russian Roulette, and the Incomplete q-Eulerian Polynomials. Cori, Robert and Mazoyer, Jacques and Morvan, Michel and Mosseri, Rémy. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001), pp.193-202, 2001, DMTCS Proceedings. 〈hal-01182961〉

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