permuton

English

Etymology

Introduced by Carlos Hoppen, Yoshiharu Kohayakawa, Carlos Gustavo Moreira, Balázs Ráth and Rudini Menezes Sampaio in their 2011 paper, "Limits of permutation sequences", with the name "limit permutation". The term "permuton" was coined by Roman Glebov, Andrzej Grzesik, Tereza Klimošová and Daniel Kráľ in their 2013 paper, "Finitely forcible graphons and permutons", from permute, to resemble graphon.

Noun

permuton (plural permutons)

1. (mathematics, physics) A probability measure Φ on the σ-algebra of Borel sets of the unit square [0,1]² such that Φ has uniform marginals (that is, Φ ([α, β] × [0,1]) = Φ ([0,1] × [α, β]) = β − α for every 0 ≤ α ≤ β ≤ 1).
   • 2016, Frédérique Bassino, Mathilde Bouvel, Valentin Féray, Lucas Gerin, Adeline Pierrot, “The Brownian limit of separable permutations”, in arXiv‎^[1]:

     In the recent terminology of permutons, our work can be interpreted as the convergence of uniform random separable permutations towards a "Brownian separable permuton"..