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- Michael H. Albert, Mike D. Atkinson
- Discrete Mathematics
- 2005

A simple permutation is one that does not map any non-trivial interval onto an interval. It is shown that, if the number of simple permutations in a pattern restricted class of permutations isâ€¦ (More)

- Mike D. Atkinson, Maximillian M. Murphy, Nikola Ruskuc
- Order
- 2002

It is known that the \pattern containment" order on permutations is not a partial well-order. Nevertheless, many naturally de ned subsets of permutations are partially well-ordered, in which caseâ€¦ (More)

- Mike D. Atkinson, Timothy Stitt
- Discrete Mathematics
- 2002

Restricted permutations are those constrained by having to avoid subsequences ordered in various prescribed ways. A closed set is a set of permutations all satisfying a given basis set ofâ€¦ (More)

- Mike D. Atkinson
- Electr. J. Comb.
- 1998

It is shown that there are ? 2n n ? P n?1 m=0 2 n?m?1 ? 2m m permutations which are the union of an increasing sequence and a decreasing sequence .

- Mike D. Atkinson, Maximillian M. Murphy, Nikola Ruskuc
- Theor. Comput. Sci.
- 2002

- Mike D. Atkinson, JÃ¶rg-RÃ¼diger Sack, Nicola Santoro, Thomas Strothotte
- Commun. ACM
- 1986

A simple implementation of double-ended priority queues is presented. The proposed structure, called a min-max heap, can be built in linear time; in contrast to conventional heaps, it allowsâ€¦ (More)

- Michael H. Albert, Mike D. Atkinson, Chris C. Handley, Derek A. Holton, Walter Stromquist
- Electr. J. Comb.
- 2002

The density of a permutation pattern Ï€ in a permutation Ïƒ is the proportion of subsequences of Ïƒ of length |Ï€| that are isomorphic to Ï€. The maximal value of the density is found for several patternsâ€¦ (More)

- Mike D. Atkinson, Maximillian M. Murphy, Nikola Ruskuc
- Electr. J. Comb.
- 2005

Pattern avoidance classes of permutations that cannot be expressed as unions of proper subclasses can be described as the set of subpermutations of a single bijection. In the case that this bijectionâ€¦ (More)

We consider the problem of developing algorithms for the recognition of a xed pattern within a permutation. These methods are based upon using a carefully chosen chain or tree of subpatterns to buildâ€¦ (More)

- Mike D. Atkinson
- Inf. Process. Lett.
- 1981

The famous Towers of Hanoi puzzle consists of 3 pegs (A, B, C) on one of which (A) are stacked n rings of different sizes, each ring resting on a larger ring. The objective is to move the n rings oneâ€¦ (More)