Geodesic
Counting Multiple Cyclic Choices Without Adjacencies
Canadian mathematical bulletin, Tome 48 (2005) no. 2, pp. 244-250

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We give a particularly elementary solution to the following well-known problem. What is the number of $k$ -subsets $X\subseteq {{I}_{n}}=\left\{ 1,2,3,\ldots ,n \right\}$ 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.
DOI : 10.4153/CMB-2005-022-4
Mots-clés : 05A19, 05A05 
McLeod, Alice; Moser, William. Counting Multiple Cyclic Choices Without Adjacencies. Canadian mathematical bulletin, Tome 48 (2005) no. 2, pp. 244-250. doi: 10.4153/CMB-2005-022-4
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     author = {McLeod, Alice and Moser, William},
     title = {Counting {Multiple} {Cyclic} {Choices} {Without} {Adjacencies}},
     journal = {Canadian mathematical bulletin},
     pages = {244--250},
     year = {2005},
     volume = {48},
     number = {2},
     doi = {10.4153/CMB-2005-022-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-022-4/}
}
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