Variants of pop-stack sorting
February 15, 2022
The purpose of this talk is to advertise noninvertible combinatorial dynamics, a largely unexplored area with several interesting directions. We will focus on the pop-stack sorting map, a specific noninvertible operator on the symmetric group, along with several of its recently-defined variants. We will discuss generalizations and extensions of the pop-stack sorting map to Coxeter groups and meet-semilattices. We will also see how to use pop-stack sorting to extend the definition of rowmotion to meet-semidistributive lattices; the resulting rowmotion operators are not always invertible. Finally, we will consider "dual" versions of the Coxeter group pop-stack sorting operators called Coxeter pop-tsack torsing operators. The discussions of rowmotion for meet-semidistributive lattices and Coxeter pop-tsack torsing are based on joint work with Nathan Williams.