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» On Trees and Noncrossing Partitions
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COMBINATORICS
1998
42views more  COMBINATORICS 1998»
13 years 5 months ago
On Noncrossing and Nonnesting Partitions for Classical Reflection Groups
The number of noncrossing partitions of {1, 2, . . . , n} with fixed block sizes has a simple closed form, given by Kreweras, and coincides with the corresponding number for nonne...
Christos A. Athanasiadis
DM
2008
82views more  DM 2008»
13 years 5 months ago
2-Binary trees: Bijections and related issues
A 2-binary tree is a binary rooted tree whose root is colored black and the other vertices are either black or white. We present several bijections concerning different types of 2...
Nancy S. S. Gu, Nelson Y. Li, Toufik Mansour
JCT
2011
87views more  JCT 2011»
13 years 7 days ago
Chain enumeration of k-divisible noncrossing partitions of classical types
We give combinatorial proofs of the formulas for the number of multichains in the k-divisible noncrossing partitions of classical types with certain conditions on the rank and the ...
Jang Soo Kim
DM
2006
91views more  DM 2006»
13 years 5 months ago
Restricted Dumont permutations, Dyck paths, and noncrossing partitions
We complete the enumeration of Dumont permutations of the second kind avoiding a pattern of length 4 which is itself a Dumont permutation of the second kind. We also consider some ...
Alexander Burstein, Sergi Elizalde, Toufik Mansour
COMBINATORICS
2000
107views more  COMBINATORICS 2000»
13 years 5 months ago
Counting Pattern-free Set Partitions II: Noncrossing and Other Hypergraphs
A (multi)hypergraph H with vertices in N contains a permutation p = a1a2 . . . ak of 1, 2, . . . , k if one can reduce H by omitting vertices from the edges so that the resulting ...
Martin Klazar