Promotion and cyclic sieving via webs
  We show that Sch\"utzenberger's promotion on two and three row rectangular Young tableaux can be realized as cyclic rotation of certain planar graphs introduced by Kuperberg. Moreover, following work of the third author, we show that this action admits the cyclic sieving phenomenon. 
T. Kyle Petersen, Pavlo Pylyavskyy, and Brendon Rhoades