Abstract
A non-crossing tree is a tree drawn on the plane having as vertices a set of points on the boundary of a circle, and whose edges are straight line segments and do not cross. Continuing previous research on non-crossing trees, we study several new statistics: number of endpoints, number of boundary edges, maximum degree, height and path-length. In some cases we obtain closed formulas while in others we deduce asymptotic estimates. Our approach is based on generating functions and on several bijections between NC-trees and various other combinatorial objects.
Partially supported by Project No. 98191 of the USA-Spain Commission for Scientific Cooperation and by Proyecto PB98-0933.
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Deutsch, E., Noy, M. (2000). New Statistics on Non-crossing Trees. In: Krob, D., Mikhalev, A.A., Mikhalev, A.V. (eds) Formal Power Series and Algebraic Combinatorics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04166-6_65
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DOI: https://doi.org/10.1007/978-3-662-04166-6_65
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