Noncrossing Trees and Noncrossing Graphs

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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.
7 pages, 5 figures

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Combinatorics, 05A05, 05C30

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http://salesiana.dossiersoluciones.com/handle/123456789/95192

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0509715
 http://arxiv.org/abs/math/0509715

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arXiv