Promotion and evacuation on standard young tableaux of rectangle and staircase shape

Abstract

(Dual-)promotion and (dual-)evacuation are bijections on SYT(λ) for any partition λ. Let cr denote the rectangular partition (c,. . ., c) of height r, and let sck (k > 2) denote the staircase partition (k, k-1,. . ., 1). We demonstrate a promotion-and evacuation-preserving embedding of SYT(sck) into SYT(kk+1). We hope that this result, together with results by Rhoades on rectangular tableaux, can help to demonstrate the cyclic sieving phenomenon of promotion action on SYT(sck).