Toric promotion

Authors :: Defant, Colin
Source :: Proceedings of the American Mathematical Society. 151:45-57
Publication Year :: 2022
Publisher :: American Mathematical Society (AMS), 2022.
Abstract: We introduce toric promotion as a cyclic analogue of Sch\"utzenberger'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.<br />Comment: 10 pages, 5 figures, to be published in Proceedings of the AMS