Braid graphs in simply-laced triangle-free Coxeter systems are partial cubes

Any two reduced expressions for the same Coxeter group element are related by a sequence of commutation and braid moves. We say that two reduced expressions are braid equivalent if they are related via a sequence of braid moves, and the corresponding equivalence classes are called braid classes. Each braid class can be encoded in terms of a braid graph in a natural way. In this paper, we study the structure of braid graphs in simply-laced Coxeter systems. We prove that every reduced expression has a unique factorization as a product of so-called links, which in turn induces a decomposition of the braid graph into a box product of the braid graphs for each link factor. When the Coxeter graph has no three-cycles, we use the decomposition to prove that braid graphs are partial cubes, i.e., can be isometrically embedded into a hypercube. For a special class of links, called Fibonacci links, we prove that the corresponding braid graphs are Fibonacci cubes.Comment: 24 page, 11 figure

Who teaches writing?

Who Teaches Writing is an open teaching and learning resource being used in English Composition classes at Oklahoma State University. It was authored by contributors from Oklahoma State University and also includes invited chapters from other institutions both inside and outside of Oklahoma. Contributors include faculty from various departments, contingent faculty and staff, and graduate instructors. One purpose of the resource is to provide short, relatively jargon-free chapters geared toward undergraduate students taking First-Year Composition. Support for this project was provided in part by OpenOKState and Oklahoma State University Libraries.OpenOKStateOklahoma State University LibrariesLibraryEnglis