EJC
2011
12 years 11 months ago
2011
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...
COMBINATORICS
2002
13 years 4 months ago
2002
: 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...
COMBINATORICS
2002
13 years 4 months ago
2002
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...
COMBINATORICS
2004
13 years 4 months ago
2004
Haglund and Loehr previously conjectured two equivalent combinatorial formulas for the Hilbert series of the Garsia-Haiman diagonal harmonics modules. These formulas involve weigh...
JCT
2007
13 years 4 months ago
2007
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...
COMBINATORICS
2007
13 years 4 months ago
2007
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 (...
COMBINATORICS
2007
13 years 4 months ago
2007
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...
EJC
2008
13 years 4 months ago
2008
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...
DMTCS
2008
13 years 4 months ago
2008
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...
DM
2008
13 years 4 months ago
2008
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-...