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The Insertion Encoding of Permutations
Applications of the insertion encoding to the evaluation of generating functions for classes of permutations, construction of polynomial time algorithms for enumerating such classes, and the illustration of bijective equivalence between classes are demonstrated.
Generic SBDD Using Computational Group Theory
We introduce a novel approach for symmetry breaking by dominance detection (SBDD). The essence of SBDD is to perform 'dominance checks' at each node in a search tree to ensure that no symmetrically…
On groups which act freely and properly on finite dimensional homotopy spheres
Growing at a Perfect Speed
A collection of permutation classes is exhibited whose growth rates form a perfect set, thereby refuting some conjectures of Balogh, Bollobás and Morris.
Tractable Symmetry Breaking Using Restricted Search Trees
A new conceptual abstraction in symmetry breaking - the GE-tree is presented, and a polynomial-time algorithm for this construction in the case of CSPs with arbitrary value symmetries is given.
On vector enumeration
- S. Linton
- Mathematics, Computer Science
- 1 October 1993
Counting cases in substitope algorithms
- D. Banks, S. Linton, P. Stockmeyer
- Computer ScienceIEEE Transactions on Visualization and Computer…
- 1 July 2004
It is shown how Polya theory produces a closed-form upper bound on the case counts, and how this produces a generic visualization algorithm to produce substitopes (geometric substitutions of polytopes) using "GAP," a software system for computational group theory.
Finding the smallest image of a set
- S. Linton
- MathematicsISSAC '04
- 4 July 2004
An algorithm for finding a canonical image of a set of points under the action of a permutation group that has applications to combinatorial and other search problems, allowing isomorphic results to be eliminated more efficiently.
Conditional Symmetry Breaking
- Ian P. Gent, T. Kelsey, S. Linton, Iain McDonald, I. Miguel, Barbara M. Smith
- Computer ScienceCP
- 1 October 2005
It is demonstrated experimentally that three methods, well-known for breaking unconditional symmetries, can be applied to conditional symmetry breaking, and three methods are augmenting the search process to break the conditional symmetry dynamically through the use of a variant of Symmetry Breaking by Dominance Detection (SBDD).
This volume contains a mixture of survey and research articles by leading experts, whom include the two invited speakers, Martin Klazar and Mike Atkinson, covering all the significant strands of current research in permutation patterns.