Bijections for rhombic alternative tableaux
arXiv:2603.12700
Abstract
We generalize well-known bijections between alternative tableaux and permutations to bijections between rhombic alternative tableaux (RAT) and assemblées of permutations. We show how these various bijections are connected. As a consequence, we find a refined enumeration formula for RAT. One of our bijections carries many statistics from RAT to assemblées; notably, it sends the number of free cells to the number of crossings, which answers a question of Mandelshtam and Viennot. We also find an -to- map from marked Laguerre histories to assemblées, answering a question of Corteel and Nunge.
38 pages, 18 figures