Catalan Numbers for the Classroom?
✍ Scribed by Judita Cofman
- Publisher
- Birkhäuser-Verlag
- Year
- 1997
- Weight
- 514 KB
- Volume
- 52
- Category
- Article
- ISSN
- 0013-6018
No coin nor oath required. For personal study only.
📜 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
A new combinatorial interpretation is presented for generalized Catalan numbers [11], i.e., C¢(~) enumerates the collection of divisions of (~, fi) pints on the circumference of a circle into n~ set of v~-point-groups (1 ~<i ~<k) without "crossing".
We prove that the number of PGL(2. C) equivalence classes of degree d rational maps with a fixed branch set is generically equal to the "Catalan number" p(d) = (l/d)( 2j:f). Several (previously known) applications of Catalan numbers to combinatorics and algebraic geometry are discussed throughout t