| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 6423747 | Electronic Notes in Discrete Mathematics | 2016 | 6 Pages |
Abstract
We present production matrices for non-crossing geometric graphs on point sets in convex position, which allow us to derive formulas for the numbers of such graphs. Several known identities for Catalan numbers, Ballot numbers, and Fibonacci numbers arise in a natural way, and also new formulas are obtained, such as a formula for the number of non-crossing geometric graphs with root vertex of given degree. The characteristic polynomials of some of these production matrices are also presented. The proofs make use of generating trees and Riordan arrays.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Clemens Huemer, Carlos Seara, Rodrigo I. Silveira, Alexander Pilz,