Toric Promotion

Abstract

We introduce toric promotion as a cyclic analogue of Schützenberger's promotion operator. Toric promotion acts on the set of labelings of a graph $G$. We discuss connections between toric promotion and previously-studied notions such as toric posets and friends-and-strangers graphs. Our main theorem provides a surprisingly simple description of the orbit structure of toric promotion when $G$ is a forest.

10 pages, 5 figures, to be published in Proceedings of the AMS