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COMBINATORICS
2007
87views more  COMBINATORICS 2007»
13 years 4 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
JCT
2010
112views more  JCT 2010»
13 years 3 months ago
Annular embeddings of permutations for arbitrary genus
In the symmetric group on a set of size 2n, let P2n denote the conjugacy class of involutions with no fixed points (equivalently, we refer to these as “pairings”, since each ...
I. P. Goulden, William Slofstra
JCT
2007
97views more  JCT 2007»
13 years 4 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
CEC
2010
IEEE
13 years 2 months ago
A hybrid multi-objective extremal optimisation approach for multi-objective combinatorial optimisation problems
Extremal optimisation (EO) is a relatively recent nature-inspired heuristic whose search method is especially suitable to solve combinatorial optimisation problems. To date, most o...
Pedro Gómez-Meneses, Marcus Randall, Andrew...