### 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.

Original language | English |
---|---|

Pages (from-to) | 301-306 |

Number of pages | 6 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 54 |

DOIs | |

Publication status | Published - 1 Oct 2016 |

Externally published | Yes |

### Fingerprint

### Keywords

- Catalan number
- geometric graph
- production matrix
- Riordan array

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Electronic Notes in Discrete Mathematics*,

*54*, 301-306. https://doi.org/10.1016/j.endm.2016.09.052

**Production matrices for geometric graphs.** / Huemer, Clemens; Seara, Carlos; Silveira, Rodrigo I.; Pilz, Alexander.

Research output: Contribution to journal › Article › Research › peer-review

*Electronic Notes in Discrete Mathematics*, vol. 54, pp. 301-306. https://doi.org/10.1016/j.endm.2016.09.052

}

TY - JOUR

T1 - Production matrices for geometric graphs

AU - Huemer, Clemens

AU - Seara, Carlos

AU - Silveira, Rodrigo I.

AU - Pilz, Alexander

PY - 2016/10/1

Y1 - 2016/10/1

N2 - 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.

AB - 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.

KW - Catalan number

KW - geometric graph

KW - production matrix

KW - Riordan array

UR - http://www.scopus.com/inward/record.url?scp=84992555106&partnerID=8YFLogxK

U2 - 10.1016/j.endm.2016.09.052

DO - 10.1016/j.endm.2016.09.052

M3 - Article

VL - 54

SP - 301

EP - 306

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

SN - 1571-0653

ER -