DMTCS Proceedings, Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001

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DMTCS Conference vol AA (2001), pp. 193-202

DMTCS

Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001

Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.)

DMTCS Conference Volume AA (2001), pp. 193-202


author: Travis Herbranson and Don Rawlings
title: A Sequential Search Distribution: Proofreading, Russian Roulette, and the Incomplete
q
-Eulerian Polynomials
keywords: California Polytechnic State University, San Luis Obispo, California 93407
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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reference: Travis Herbranson and Don Rawlings (2001), A Sequential Search Distribution: Proofreading, Russian Roulette, and the Incomplete
q
-Eulerian Polynomials, in Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AA, pp. 193-202
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