Combinatorial analysis of ramified patterns and computer imagery of trees
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Trees everywhere (invited lecture)
CAAP '90 Proceedings of the fifteenth colloquium on CAAP'90
Average-case analysis of algorithms and data structures
Handbook of theoretical computer science (vol. A)
Faster communication in known topology radio networks
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
An approximation algorithm for conflict-aware broadcast scheduling in wireless ad hoc networks
Proceedings of the 9th ACM international symposium on Mobile ad hoc networking and computing
Optimal gossiping with unit size messages in known topology radio networks
CAAN'06 Proceedings of the Third international conference on Combinatorial and Algorithmic Aspects of Networking
Faster centralized communication in radio networks
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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The Strahler number of binary trees has been introduced by hydrogeologists and rediscovered in computer science in relation with some optimization problems. Explicit expressions have been given for the Strahler distribution, i.e. binary trees enumerated by number of vertices and Strahler number. Two other Strahler distributions have been discovered with the logarithmic height of Dyck paths and the pruning number of forests of planar trees in relation with molecular biology. Each of these three classes are enumerated by the Catalan numbers, but only two bijections preserving the Strahler parameters have been explicited: by Françon between binary trees and Dyck paths, by Zeilberger between binary trees and forests of planar trees. We present here the missing bijection between forests of planar trees and Dyck paths sending the pruning number onto the logarithmic height. A new functional equation for the Strahler generating function is deduced. Some orthogonal polynomials appear, they are one parameter Tchebycheff polynomials.