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

2010/03/13 by Steven Pon, Qiang Wang, Pon, Steven +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1003.2728

14 pages, typos corrected

openalex publication_date 2010/03/13 · arxiv created 2010/08/09 · arxiv updated 2015/03/13 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

(Dual-)promotion and (dual-)evacuation are bijections on SYT(λ) for any partition λ. Let c^r denote the rectangular partition (c,...,c) of height r, and let sc_k (k > 2) denote the staircase partition (k,k-1,...,1). B. Rhoades showed representation-theoretically that promotion on SYT(c^r) exhibits the cyclic sieving phenomenon (CSP). In this paper, we demonstrate a promotion- and evacuation-preserving embedding of SYT(sc_k) into SYT(k^k+1). This arose from an attempt to demonstrate the CSP of promotion action on SYT(sc_k).

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