Noncrossing Trees and Noncrossing Graphs

Details Noncrossing Trees and Noncrossing Graphs Noncrossing Trees and Noncrossing Graphs

2005-09-30

arxiv.org/abs/math/0509715v1

Mathematics

Combinatorics

7 pages, 5 figures

Scientific paper

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.

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