Analysis of the gift exchange problem
| Autor: | David Applegate, Doron Zeilberger, Moa Apagodu, Neil J. A. Sloane |
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| Rok vydání: | 2017 |
| Předmět: |
Applied Mathematics
Integer sequence Subject (documents) Resolution (logic) 05A 11B37 33F10 Theoretical Computer Science Combinatorics Computational Theory and Mathematics Bessel polynomials Encyclopedia FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Geometry and Topology Combinatorics (math.CO) Mathematics |
| DOI: | 10.48550/arxiv.1701.08394 |
| Popis: | In the gift exchange game there are n players and n wrapped gifts. When a player's number is called, that person can either choose one of the remaining wrapped gifts, or can "steal" a gift from someone who has already unwrapped it, subject to the restriction that no gift can be stolen more than a total of sigma times. The problem is to determine the number of ways that the game can be played out, for given values of sigma and n. Formulas and asymptotic expansions are given for these numbers. This work was inspired in part by a 2005 remark by Robert A. Proctor in the On-Line Encyclopedia of Integer Sequences. Comment: 14 pages, 2 tables. arXiv admin note: substantial text overlap with arXiv:0907.0513 |
| Databáze: | OpenAIRE |
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