Vol. 12, No. 4, 2019

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Positional strategies in games of best choice

Aaron Fowlkes and Brant Jones

Vol. 12 (2019), No. 4, 647–658
DOI: 10.2140/involve.2019.12.647
Abstract

We study a variation of the game of best choice (also known as the secretary problem or game of googol) under an additional assumption that the ranks of interview candidates are restricted using permutation pattern-avoidance. We describe the optimal positional strategies and develop formulas for the probability of winning.

Keywords
secretary problem, random permutation, permutation pattern
Mathematical Subject Classification 2010
Primary: 05A05, 91A60
Milestones
Received: 25 February 2018
Revised: 23 October 2018
Accepted: 4 December 2018
Published: 16 April 2019

Communicated by Kenneth S. Berenhaut
Authors
Aaron Fowlkes
Department of Mathematics
University of South Carolina
Columbia, SC
United States
Brant Jones
Department of Mathematics and Statistics
James Madison University
Harrisonburg, VA
United States