2 citations · 4 across the 4 of their papers we have counts for
4 papers
A Family of Minimal and Renormalizable Rectangle Exchange Maps
Ian Alevy, Richard Kenyon, Ren Yi
A domain exchange map (DEM) is a dynamical system defined on a smooth Jordan domain which is a piecewise translation. We explain how to use cut-and-project sets to construct minima…
The Triple Lattice PETs
Ren Yi
Polytope exchange transformations (PETs) are higher dimensional generalizations of interval exchange transformations (IETs) which have been well-studied for more than 40 years. A g…
The Tetrahedral Twists
Ren Yi
We introduce a family of piecewise isometries parametrized by on the surface of a regular tetrahedron, which we call the tetrahedral twists. This family of maps…
The Alexander and Jones Polynomials Through Representations of Rook Algebras
Stephen Bigelow, Eric Ramos, Ren Yi
In the 1920's Artin defined the braid group in an attempt to understand knots in a more algebraic setting. A braid is a certain arrangement of strings in three-dimensional space. I…