Permutations on the Random Permutation
Copyright policy )Permutations on the Random Permutation
The random permutation is the Fraïssé limit of the class of finite structures with two linear orders. Answering a problem stated by Peter Cameron in 2002, we use a recent Ramsey-theoretic technique to show that there exist precisely 39 closed supergroups of the automorphism group of the random permutation, and thereby expose all symmetries of this structure. Equivalently, we classify all structures which have a first-order definition in the random permutation.
reduct, Permutations, words, matrices, random permutation, Ramsey theory, Model-theoretic algebra, Mathematics - Logic, Models of other mathematical theories, Model theory of denumerable and separable structures, Combinatorics of partially ordered sets, Groups as automorphisms of other structures, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Logic (math.LO), canonical function
reduct, Permutations, words, matrices, random permutation, Ramsey theory, Model-theoretic algebra, Mathematics - Logic, Models of other mathematical theories, Model theory of denumerable and separable structures, Combinatorics of partially ordered sets, Groups as automorphisms of other structures, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Logic (math.LO), canonical function
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