We prove various congruences for Catalan and Motzkin numbers as well as related sequences. The common thread is that all these sequences can be expressed in terms of binomial coefficients. Our techniques are combinatorial and algebraic: group actions, induction, and Lucas' congruence for binomial co
Sum-Difference Sequences and Catalan Numbers
β Scribed by Martin Aigner; Volker Schulze
- Publisher
- Springer Vienna
- Year
- 1999
- Tongue
- English
- Weight
- 171 KB
- Volume
- 127
- Category
- Article
- ISSN
- 0026-9255
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A class of numbers, called Catalan-like numbers, are introduced which unify many well-known counting coefficients, such as the Catalan numbers, the Motzkin numbers, the middle binomial coefficients, the hexagonal numbers, and many more. Generating functions, recursions and determinants of Hankel mat
It is known that a convex polygon of n sides admits C.-2 triangulations, where C, is a Catalan number. We classify these triangulations (considered as outerplanar graphs) according to their dual trees, and prove the following formula for the number of triangulations of a convex n-gon whose dual tree