New Statistics on Non-crossing Trees

Emeric Deutsch () and Marc Noy ()
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Emeric Deutsch: Polytechnic University
Marc Noy: Universitat Politècnica de Catalunya

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 667-676 from Springer

Abstract: 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.

Date: 2000
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DOI: 10.1007/978-3-662-04166-6_65

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