Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775445 | Advances in Applied Mathematics | 2017 | 18 Pages |
Abstract
In this paper, we investigate the weighted Catalan, Motzkin and Schröder numbers together with the corresponding weighted paths. The relation between these numbers is illustrated by three equations, which also lead to some known and new interesting identities. To show these three equations, we provide combinatorial proofs. One byproduct is to find a bijection between two sets of Catalan paths: one consisting of those with k valleys, and the other consisting of kN steps in even positions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Zhi Chen, Hao Pan,