Generating permutations with given ups and downs
Discrete Applied Mathematics
Generating trees and the Catalan and Schro¨der numbers
Discrete Mathematics
Forbidden subsequences and Chebyshev polynomials
Discrete Mathematics - Special issue on selected papers in honor of Henry W. Gould
From Motzkin to Catalan permutations
Discrete Mathematics
Permutations with forbidden subsequences and a generalized Schröder number
Discrete Mathematics
Communications of the ACM
Loopless generation of up-down permutations
Discrete Mathematics
A CAT algorithm for generating permutations with a fixed number of inversions
Information Processing Letters
A loopless algorithm for generating the permutations of a multiset
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
Combinatorics of Permutations
Constant time generation of derangements
Information Processing Letters
Discrete Applied Mathematics
A general exhaustive generation algorithm for Gray structures
Acta Informatica
Some Generalizations of a Simion–Schmidt Bijection
The Computer Journal
Combinatorial Gray codes for classes of pattern avoiding permutations
Theoretical Computer Science
| Hi-index | 0.89 |
In a recent article [W.M.B. Dukes, M.F. Flanagan, T. Mansour, V. Vajnovszki, Combinatorial Gray codes for classes of pattern avoiding permutations, Theoret. Comput. Sci. 396 (2008) 35-49], Dukes, Flanagan, Mansour and Vajnovszki present Gray codes for several families of pattern avoiding permutations. In their Gray codes two consecutive objects differ in at most four or five positions, which is not optimal. In this paper, we present a unified construction in order to refine their results (or to find other Gray codes). In particular, we obtain more restrictive Gray codes for the two Wilf classes of Catalan permutations of length n; two consecutive objects differ in at most two or three positions which is optimal for n odd. Other refinements have been found for permutation sets enumerated by the numbers of Schroder, Pell, even index Fibonacci numbers and the central binomial coefficients. A general efficient generating algorithm is also given.