Add to ORKGWe 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
AbstractThis paper describes a systematic approach to the enumeration of ‘non-crossing’ geometric co...
Given a set $P$ of points in the plane, the geometric tree graph of $P$ is defined as the graph $T...
AbstractGiven a set P of points in the plane, the geometric tree graph of P is defined as the graph ...
We present production matrices for non-crossing geometric graphs on point sets in convex position, w...
We present production matrices for non-crossing geometric graphs on point sets in convex position, w...
We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-...
We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-...
We propose the study of counting problems for geometric graphs defined on point sets in convex posit...
We use production matrices to count several classes of geometric graphs. We present novel production...
An n×n production matrix for a class of geometric graphs has the property that the numbers of these ...
We propose the study of counting problems for geometric graphs defined on point sets in convex posit...
We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-...
We use the concept of production matrices to show that there exist sets of n points in the plane tha...
We use the concept of production matrices to show that there exist sets of n points in the plane tha...
We use the concept of production matrices to show that there exist sets of n points in the plane tha...
AbstractThis paper describes a systematic approach to the enumeration of ‘non-crossing’ geometric co...
Given a set $P$ of points in the plane, the geometric tree graph of $P$ is defined as the graph $T...
AbstractGiven a set P of points in the plane, the geometric tree graph of P is defined as the graph ...
We present production matrices for non-crossing geometric graphs on point sets in convex position, w...
We present production matrices for non-crossing geometric graphs on point sets in convex position, w...
We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-...
We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-...
We propose the study of counting problems for geometric graphs defined on point sets in convex posit...
We use production matrices to count several classes of geometric graphs. We present novel production...
An n×n production matrix for a class of geometric graphs has the property that the numbers of these ...
We propose the study of counting problems for geometric graphs defined on point sets in convex posit...
We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-...
We use the concept of production matrices to show that there exist sets of n points in the plane tha...
We use the concept of production matrices to show that there exist sets of n points in the plane tha...
We use the concept of production matrices to show that there exist sets of n points in the plane tha...
AbstractThis paper describes a systematic approach to the enumeration of ‘non-crossing’ geometric co...
Given a set $P$ of points in the plane, the geometric tree graph of $P$ is defined as the graph $T...
AbstractGiven a set P of points in the plane, the geometric tree graph of P is defined as the graph ...