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Counting Multiple Cyclic Choices Without Adjacencies

  Published:2005-06-01
 Printed: Jun 2005
  • Alice McLeod
  • William Moser
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Abstract

We give a particularly elementary solution to the following well-known problem. What is the number of $k$-subsets $X \subseteq I_n=\{1,2,3,\dots,n\}$ satisfying ``no two elements of $X$ are adjacent in the circular display of $I_n$''? Then we investigate a new generalization (multiple cyclic choices without adjacencies) and apply it to enumerating a class of 3-line latin rectangles.
MSC Classifications: 05A19, 05A05 show english descriptions Combinatorial identities, bijective combinatorics
Permutations, words, matrices
05A19 - Combinatorial identities, bijective combinatorics
05A05 - Permutations, words, matrices
 

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