# 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 is finite, the class has an algebraic generating function and is defined by a finite set of restrictions. Some partial results on classes with an infinite number of(More)
• Electr. J. Comb.
• 2002
The density of a permutation pattern π in a permutation σ is the proportion of subsequences of σ of length |π| that are isomorphic to π. The maximal value of the density is found for several patterns π, and asymptotic upper and lower bounds for the maximal density are found in several other cases. The results are generalised to sets of patterns and the(More)
• 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 case they have a strong nite basis property. Several classes are proved to be partially well-ordered under pattern containment. Conversely, a number of new antichains(More)
A simple permutation is one which maps no proper non-singleton interval onto an interval. We consider the enumeration of simple permutations from several aspects. Our results include a straightforward relationship between the ordinary generating function for simple permutations and that for all permutations, that the coefficients of this series are not P(More)
• 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 allows both</italic> FindMin <italic>and</italic> FindMax <italic>to be performed in constant time;</italic> Insert, DeleteMin, <italic>and</italic> DeleteMax(More)
• Inf. Process. Lett.
• 1992
Atkinson, M.D. and J.-R. Sack, Generating binary trees at random, Information Processing Letters 41 (1992) 21-23. We give a new constructive proof of the Chung-Feller theorem. Our proof provides a new and simple linear-time algorithm for generating random binary trees on n nodes; the algorithm uses integers no larger than 212.
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 build up the entire pattern. Generally, large improvements over brute force search can be obtained. Even using on-line versions of these methods provides such(More)