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EJC
2011
13 years 6 months ago
Enumeration of connected Catalan objects by type
Noncrossing set partitions, nonnesting set partitions, Dyck paths, and rooted plane trees are four classes of Catalan objects which carry a notion of type. There exists a product f...
Brendon Rhoades
COMBINATORICS
2002
92views more  COMBINATORICS 2002»
13 years 11 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
COMBINATORICS
2002
104views more  COMBINATORICS 2002»
13 years 11 months ago
Exchange Symmetries in Motzkin Path and Bargraph Models of Copolymer Adsorption
In a previous work [26], by considering paths that are partially weighted, the generating function of Dyck paths was shown to possess a type of symmetry, called an exchange relati...
E. J. Janse van Rensburg, A. Rechnitzer
COMBINATORICS
2004
96views more  COMBINATORICS 2004»
13 years 11 months ago
Conjectured Combinatorial Models for the Hilbert Series of Generalized Diagonal Harmonics Modules
Haglund and Loehr previously conjectured two equivalent combinatorial formulas for the Hilbert series of the Garsia-Haiman diagonal harmonics modules. These formulas involve weigh...
Nicholas A. Loehr, Jeffrey B. Remmel
JCT
2007
97views more  JCT 2007»
13 years 11 months ago
What power of two divides a weighted Catalan number?
Given a sequence of integers b = (b0,b1,b2,...) one gives a Dyck path P of length 2n the weight wt(P) = bh1 bh2 ···bhn , where hi is the height of the ith ascent of P. The corr...
Alexander Postnikov, Bruce E. Sagan
COMBINATORICS
2007
85views more  COMBINATORICS 2007»
13 years 11 months ago
Asymptotics of the Average Height of 2-Watermelons with a Wall
We generalize the classical work of de Bruijn, Knuth and Rice (giving the asymptotics of the average height of Dyck paths of length n) to the case of p–watermelons with a wall (...
Markus Fulmek
COMBINATORICS
2007
87views more  COMBINATORICS 2007»
13 years 11 months ago
A Bijection on Dyck Paths and its Cycle Structure
The known bijections on Dyck paths are either involutions or have notoriously intractable cycle structure. Here we present a size-preserving bijection on Dyck paths whose cycle st...
David Callan
EJC
2008
13 years 11 months ago
Dyck paths with coloured ascents
We introduce a notion of Dyck paths with coloured ascents. For several ways of colouring, when the set of colours is itself some class of lattice paths, we establish bijections be...
Andrei Asinowski, Toufik Mansour
DMTCS
2008
83views Mathematics» more  DMTCS 2008»
13 years 11 months ago
The Location of the First Maximum in the First Sojourn of a Dyck Path
For Dyck paths (nonnegative symmetric) random walks, the location of the first maximum within the first sojourn is studied. Generating functions and explicit resp. asymptotic expre...
Helmut Prodinger
DM
2008
113views more  DM 2008»
13 years 11 months ago
Multivariate Fuss-Catalan numbers
Catalan numbers C(n) = 1 n+1 2n n enumerate binary trees and Dyck paths. The distribution of paths with respect to their number k of factors is given by ballot numbers B(n, k) = n-...
Jean-Christophe Aval