scholarly journals Parity reversing involutions on plane trees and 2-Motzkin paths

2006 ◽  
Vol 27 (2) ◽  
pp. 283-289 ◽  
Author(s):  
William Y.C. Chen ◽  
Louis W. Shapiro ◽  
Laura L.M. Yang
Keyword(s):  
Plane Trees ◽  
Motzkin Paths

scholarly journals Bootstrapping and double-exponential limit laws

2015 ◽  
Vol Vol. 17 no. 1 (Combinatorics) ◽  
Author(s):  
Helmut Prodinger ◽  
Stephan Wagner
Keyword(s):  
Generating Functions ◽  
Maximum Degree ◽  
Exponential Rate ◽  
Limit Laws ◽  
Double Exponential Distribution ◽  
Double Exponential ◽  
Longest Run ◽  
Plane Trees ◽  
International Audience ◽  
Motzkin Paths

Combinatorics International audience We provide a rather general asymptotic scheme for combinatorial parameters that asymptotically follow a discrete double-exponential distribution. It is based on analysing generating functions Gh(z) whose dominant singularities converge to a certain value at an exponential rate. This behaviour is typically found by means of a bootstrapping approach. Our scheme is illustrated by a number of classical and new examples, such as the longest run in words or compositions, patterns in Dyck and Motzkin paths, or the maximum degree in planted plane trees.

Standard Young tableaux in a (2,1)-hook and Motzkin paths

2021 ◽  
Vol 344 (7) ◽  
pp. 112395
Author(s):  
Rosena R.X. Du ◽  
Jingni Yu
Keyword(s):  
Young Tableaux ◽  
Standard Young Tableaux ◽  
Motzkin Paths

scholarly journals Bijections for a class of labeled plane trees

2010 ◽  
Vol 31 (3) ◽  
pp. 720-732 ◽  
Author(s):  
Nancy S.S. Gu ◽  
Helmut Prodinger ◽  
Stephan Wagner
Keyword(s):  
Plane Trees

Achiral plane trees

1978 ◽  
Vol 2 (3) ◽  
pp. 189-208 ◽  
Author(s):  
Nicholas Wormald
Keyword(s):  
Plane Trees

LONDON'S PLANE TREES

The Lancet ◽  
1954 ◽  
Vol 264 (6840) ◽  
pp. 709
Author(s):  
Desmond O'Neill
Keyword(s):  
Plane Trees

scholarly journals Partitions of Complete Geometric Graphs into Plane Trees

2005 ◽  
pp. 71-81
Author(s):  
Prosenjit Bose ◽  
Ferran Hurtado ◽  
Eduardo Rivera-Campo ◽  
David R. Wood
Keyword(s):  
Geometric Graphs ◽  
Plane Trees

Plane Trees Die by Canker

2021 ◽  
pp. 53-55
Author(s):  
Maria Lodovica Gullino
Keyword(s):  
Plane Trees

On the Enumeration of Tree-Rooted Maps

1967 ◽  
Vol 19 ◽  
pp. 174-183 ◽  
Author(s):  
R. C. Mullin
Keyword(s):  
Spanning Tree ◽  
Root Vertex ◽  
Rooted Map ◽  
Plane Trees ◽  
Root Tree

It is the purpose of this paper to show that many of the enumerative techniques available for counting rooted plane trees may be extended to tree-rooted maps, that is, rooted maps in which a spanning tree is distinguished as root tree. For example, tree-rooted maps are enumerated by partition, and the average number of trees in a rooted map with n edges is determined. An enumerative similarity between Hamiltonian rooted maps (that is, rooted maps with a distinguished Hamiltonian polygon) and tree-rooted maps is discussed. A 1-1 correspondence is established between treerooted maps with n edges and Hamiltonian rooted trivalent maps with 2n + 1 vertices in which the root vertex is exceptional, being divalent, both of which are in 1-1 correspondence with non-separable Hamiltonian-rooted triangularized digons with n internal vertices, where both the latter are as defined in (2).

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