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The sock matching
problem
Sarah Gilliand, Charles Johnson, Sam Rush and Deborah Wood
Vol. 7 (2014), No. 5, 691–697
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Abstract |
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When matching socks after doing the laundry, how many unmatched socks can appear in the process of drawing one sock at a time from the basket? By connecting the problem of sock matching to the Catalan numbers, we give the probability that unmatched socks appear. We also show that, for each fixed , this probability approaches as the number of socks becomes large enough. The relation between the number of socks and the for which a given probability is first reached is also discussed, but a complete answer is open. |
Keywords
Catalan numbers, sock matching, Dyck paths
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Mathematical Subject Classification 2010
Primary: 05A15, 05A16
Secondary: 03B48, 00A69
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Milestones
Received: 21 August 2013
Accepted: 25 November 2013
Published: 1 August 2014
Communicated by Jim Haglund
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Authors |
| Sarah Gilliand | |
| Department of Biology The College of William & Mary College Station Unit 3011 P.O. Box 8793 Williamsburg, VA 23187 United States |
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| Charles Johnson | |
| Department of Mathematics The College of William & Mary P.O. Box 8795 Williamsburg, VA 23187 United States |
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| Sam Rush | |
| Department of Computer Science California Institute of Technology 1200 East California Boulevard, MS 305-16 Pasadena, CA 91125 United States |
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| Deborah Wood | |
| Department of Mathematics The College of William & Mary College Station Unit 4085 P.O. Box 8793 Williamsburg, VA 23187 United States |
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