Noncrossing Trees and Noncrossing Graphs
组合数学
2007-05-23 v1
摘要
We give a parity reversing involution on noncrossing trees that leads to a combinatorial interpretation of a formula on noncrossing trees and symmetric ternary trees in answer to a problem proposed by Hough. We use the representation of Panholzer and Prodinger for noncrossing trees and find a correspondence between a class of noncrossing trees, called proper oncrossing trees, and the set of symmetric ternary trees. The second result of this paper is a parity reversing involution on connected noncrossing graphs which leads to a relation between the number of noncrossing trees with a given number of edges and descents and the number of connected noncrossing graphs with a given number of vertices and edges.
引用
@article{arxiv.math/0509715,
title = {Noncrossing Trees and Noncrossing Graphs},
author = {William Y. C. Chen and Sherry H. F. Yan},
journal= {arXiv preprint arXiv:math/0509715},
year = {2007}
}
备注
7 pages, 5 figures