Permutations on the Random Permutation

@article{Linman2014PermutationsOT,
  title={Permutations on the Random Permutation},
  author={Julie Linman and Michael Pinsker},
  journal={Electron. J. Comb.},
  year={2014},
  volume={22},
  pages={2}
}
The random permutation is the Fraisse 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. 

Figures from this paper

Permutation groups on countable vector spaces over prime fields

We describe all closed permutation groups which act on the set of vectors of a countable vector space V over a prime field of odd order and which contain all automorphisms of V. In particular, we

Automorphism groups of linearly ordered homogeneous structures

We apply results proved in [Li19] to the linear order expansions of non-trivial free homogeneous structures and the universal n-linear order for $n\geq 2$, and prove the simplicity of their

The universal homogeneous binary tree

This work classifies the model-complete cores of the reducts of S2, that is, the relational structures with the same domain as S2 all of whose relations are first-order definable in S2.

The Universal Homogenous Binary

A partial order is called semilinear iff the upper bounds of each element are linearly ordered and any two elements have a common upper bound. There exists, up to isomorphism, a unique countable

The 42 reducts of the random ordered graph

The reducts of the random ordered graph up to first‐order interdefinability are determined.

Canonical Functions: a proof via topological dynamics

A proof of the existence of canonical functions in certain sets using topological dynamics, providing a shorter alternative to the original combinatorial argument and presenting equivalent algebraic characterisations of canonicity.

Clones and homogeneous structures

A structure A is called homogeneous, if every isomorphism between its finitely generated substructures extends to an automorphism of A. In this thesis we are studying homogeneous structures with

Ramsey classes: examples and constructions

This article is concerned with classes of relational structures that are closed under taking substructures and isomorphism, that have the joint embedding property, and that furthermore have the

NIP ω$\omega$ ‐categorical structures: The rank 1 case

  • Pierre Simon
  • Mathematics
    Proceedings of the London Mathematical Society
  • 2022
We classify primitive, rank 1, ω$\omega$ ‐categorical structures having polynomially many types over finite sets. We show that there are only finitely many such structures with a fixed number of

Complexity of Infinite-Domain Constraint Satisfaction

This monograph presents a self-contained introduction to the universal-algebraic approach to complexity classification, treating both finite and infinite-domain CSPs.

References

SHOWING 1-10 OF 23 REFERENCES

Ramsey Property of Posets and Related Structures

We study several classes of …nite posets with linear ordering. We examine these classes according to the Ramsey and the ordering property. As application we give several new extremely amenable groups

Reducts of Random Hypergraphs

Homogeneous Permutations

The paper discusses infinite generalisations of permutations, and the connection with Fra ̈ ıssé’s theory of countable homogeneous structures, and states a few open problems.

Reducts of the random partial order

Minimal functions on the random graph

The theorem is obtained by proving a Ramsey-type theorem for colorings of tuples in finite powers of the random graph, and by applying this to find regular patterns in the behavior of any function on therandom graph.

The 42 reducts of the random ordered graph

The reducts of the random ordered graph up to first‐order interdefinability are determined.

Reducts of Ramsey structures

A survey of results in model theory and theoretical computer science obtained recently by the authors in this context, which approaches the problem of classifying the reducts of countably infinite ordered homogeneous Ramsey structures in a finite language, and certain decidability questions connected with such reduCTs.

Reducts of the Henson graphs with a constant

Reducts of the random graph

  • S. Thomas
  • Mathematics
    Journal of Symbolic Logic
  • 1991
Let Γ be the unique (up to isomorphism) countable graph with the following property: (*) Given any two finite disjoint subsets U and V of Γ, there exists a vertex z ∈ Γ joined to every vertex in U

The 116 reducts of (Q, <, a)

This article aims to classify those reducts of expansions of (Q, <) by unary predicates which eliminate quantifiers, and in particular to show that, up to interdefinability, there are only finitely