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Triangular Dissections of N-Gons

Published online by Cambridge University Press:  20 November 2018

J. W. Moon  and
L. Moser
J. W. Moon
Affiliation:
University of Alberta
L. Moser
Affiliation:
University of Alberta
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Let f(n) denote the number of dissections of a regular n-gon into n-2 triangles by n-3 non-intersecting diagonals. It is known that

and that

1

for n = 3, 4, . . . , where f(2) = 1 by definition. (For pertinent references on this and related problems see, e. g. , Motzkin [2].) The object of this note is to obtain a simple expression for g(n) , the number of such dissections remaining when those which differ only by a rotation, reflection, or both are not considered as being different. For convenience we shall let g(2) = 1 and f(k) = 0 when k is not an integer.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 6 , Issue 2 , May 1963 , pp. 175 - 178
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Burnside, W., Theory of Groups of Finite Order, 2nd ed., Cambridge University Press, Cambridge, 1911. p. 191.Google Scholar
2. Motzkin, Th., Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associative products, Bull. Amer. Math. Soc., 54(1948) 352-360.Google Scholar