Noncrossing Trees and Noncrossing Graphs

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Preprint

30 September 2005

preprint
Published by arXiv in arXiv

DOI:10.48550/arXiv.math/0509715

Abstract

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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This publication has 6 references indexed in Scilit:

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