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» On the enumeration of d-minimal permutations
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JCT
2010
117views more  JCT 2010»
13 years 5 months ago
(2+2)-free posets, ascent sequences and pattern avoiding permutations
Abstract. We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2 + 2)-free posets and a certain class of involutions (or chord ...
Mireille Bousquet-Mélou, Anders Claesson, M...
EJC
2006
13 years 7 months ago
Old and young leaves on plane trees
Abstract. A leaf of a plane tree is called an old leaf if it is the leftmost child of its parent, and it is called a young leaf otherwise. In this paper we enumerate plane trees wi...
William Y. C. Chen, Emeric Deutsch, Sergi Elizalde
COMBINATORICS
2002
92views more  COMBINATORICS 2002»
13 years 7 months ago
Pattern Avoidance in Permutations: Linear and Cyclic Orders
: We generalize the notion of pattern avoidance to arbitrary functions on ordered sets, and consider specifically three scenarios for permutations: linear, cyclic and hybrid, the f...
Antoine Vella
JCT
2011
141views more  JCT 2011»
13 years 2 months ago
Bijections for Baxter families and related objects
The Baxter number Bn can be written as Bn = n k=0 Θk,n−k−1 with Θk,ℓ = 2 (k + 1)2 (k + 2) k + ℓ k k + ℓ + 1 k k + ℓ + 2 k . These numbers have first appeared in the...
Stefan Felsner, Éric Fusy, Marc Noy, David ...
CORR
2004
Springer
97views Education» more  CORR 2004»
13 years 7 months ago
Free quasi-symmetric functions, product actions and quantum field theory of partitions
Abstract. We investigate two associative products over the ring of symmetric functions related to the intransitive and Cartesian products of permutation groups. As an application, ...
Gérard Henry Edmond Duchamp, Jean-Gabriel L...