14 citations · 16 across the 6 of their papers we have counts for
7 papers
Isomorphisms between pattern classes
Michael Albert, M. D. Atkinson, Anders Claesson
Isomorphisms p between pattern classes A and B are considered. It is shown that, if p is not a symmetry of the entire set of permutations, then, to within symmetry, A is a subset o…
The enumeration of three pattern classes
M. H. Albert, M. D. Atkinson, Robert Brignall
The structure of three pattern classes Av(2143, 4321), Av(2143, 4312) and Av(1324, 4312) is determined using the machinery of monotone grid classes. This allows the permutations in…
The enumeration of permutations avoiding 2143 and 4231
Michael Albert, M. D. Atkinson, Robert Brignall
We enumerate the pattern class Av(2143,4231) and completely describe its permutations. The main tools are simple permutations and monotone grid classes.
Geometric grid classes of permutations
Michael H. Albert, M. D. Atkinson, Mathilde Bouvel +2
A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope \pm1 arranged in a rectangular pattern governed by a matrix. Us…
On the inverse image of pattern classes under bubble sort
Michael H. Albert, M. D. Atkinson, Mathilde Bouvel +2
Let B be the operation of re-ordering a sequence by one pass of bubble sort. We completely answer the question of when the inverse image of a principal pattern class under B is a p…
Permutation Classes of Polynomial Growth
M. H. Albert, M. D. Atkinson, Robert Brignall
A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of fo…