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Isomorphisms between pattern classes

Albert, M. H. and Atkinson, M. D. and Claesson, Anders (2014) Isomorphisms between pattern classes. Journal of Combinatorics, 6 (1-2). pp. 3-17. ISSN 2156-3527 (In Press)

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Abstract

Isomorphisms φ : A −→ B between pattern classes are considered. It is shown that, if φ is not a symmetry of the entire set of permutations, then, to within symmetry, A is a subset of one a small set of pattern classes whose structure, including their enumeration, is determined.