Sequences of Ordered Sets and Catalan Numbers
β Scribed by Mohammad Alzohairi
- Book ID
- 110233210
- Publisher
- Springer Netherlands
- Year
- 1998
- Tongue
- English
- Weight
- 64 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0167-8094
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
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