Promotion and evacuation on standard Young tableaux of rectangle and staircase shape (Q625380)

Summary: (Dual-)promotion and (dual-)evacuation are bijections on \(\text{SYT}(\lambda)\) for any partition \(\lambda\). Let \(c^r\) denote the rectangular partition \((c,\dots, c)\) of height \(r\), and let \(\text{sc}_k\) \((k> 2)\) denote the staircase partition \((k, k-1,\dots, 1)\). We demonstrate a promotionand evacuation-preserving embedding of \(\text{SYT}(\text{sc}_k)\) into \(\text{SYT}(k^{k+1})\). 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 \(\text{SYT}(\text{sc}_k)\).