Promotion, Webs, and Kwebs
Rebecca Patrias · Open Collections · 2021
In 2008, Petersen--Pylyavskyy--Rhoades proved that promotion on 2-row and 3-row rectangular standard Young tableaux can be realized as rotation of certain planar graphs called webs, which were introduced by Kuperberg. In this talk, we will introduce webs and their result. We will then generalize it to a larger family of webs---webs with both black and white boundary vertices. Lastly, we discuss on-going work to generalize further to the setting of K-theory combinatorics. This on-going work is joint with Oliver Pechenik, Jessica Striker, and Juliana Tymoczko.