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COMBINATORICS
2006

Noncrossing Trees and Noncrossing Graphs

8 years 11 months ago
Noncrossing Trees and Noncrossing Graphs
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 noncrossing 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 n edges and k descents and the number of connected noncrossing graphs with n + 1 vertices and m edges.
William Y. C. Chen, Sherry H. F. Yan
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where COMBINATORICS
Authors William Y. C. Chen, Sherry H. F. Yan
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