Work

Permutations on the random permutation

Year: 2014

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1405.4297

Authors: Linman, Julie, Pinsker, Michael

Institutions: University of Colorado Boulder, Université Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Laboratoire de Mathématiques d'Orsay, Laboratoire de Mathématiques Blaise Pascal, TU Wien

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2952656421

Cites: 1

Cited by: 2

Related to: 20