Published in
Elsevier, Discrete Mathematics, (47), p. 211-219, 1983
DOI: 10.1016/0012-365x(83)90091-2
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Permutations associated with billiard paths
Journal article published in 1983 by
Duane Detemple,
Jack M. Robertson
This paper is made freely available by the publisher.
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Abstract
Associated with a smooth closed convex curve , a point P on , and a natural number n⩾3, is a billiard graph whose vertices are permutations on the set {1,2,…,n}. The graph is constructed and applied to billiard properties of . Recursion properties of the graph as n increases are described with the aid of an appropriate generating function.