Noncrossing trees and noncrossing graphs
The electronic journal of combinatorics, Tome 13 (2006)
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.
@article{10_37236_1150,
author = {William Y. C. Chen and Sherry H. F. Yan},
title = {Noncrossing trees and noncrossing graphs},
journal = {The electronic journal of combinatorics},
year = {2006},
volume = {13},
doi = {10.37236/1150},
zbl = {1098.05022},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1150/}
}
William Y. C. Chen; Sherry H. F. Yan. Noncrossing trees and noncrossing graphs. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1150
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