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A correspondence between two sets of trees

โœ Scribed by David A Klarner

Book ID
118415228
Publisher
Elsevier Science
Year
1969
Weight
332 KB
Volume
72
Category
Article
ISSN
1385-7258

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We set up a one-to-one correspondence between two sets whose cardinalities are both equal to the nth Catalan number, namely, the set of triangulations of a convex (n + 2)-gon and the set of symmetric positive definite unimodular tridiagonal matrices of order n considered in [1].

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The Narayana numbers n appear twice in Volume 31 of Discrete Mathematics: They count the ordere0 trees with n edges (i.e. n+l nodes) and k leaves [1] and the noncrossing partitions of {1 ..... n} into k blocks . (In such a partition the existence of four numbers a<b<c<d such that a and c are in one