In the finite symmetric group, the Robinson–Schensted correspondence gives a bijection between the group and pairs ( P , Q ) of standard Young tableaux of the same shape. This bijection plays a central role in the combinatorics and the representation theory of the symmetric group. For example, in the language of Kazhdan–Lusztig theory, two permutations lie in the same left cell if and only if their images under Robinson–Schensted have the same tableau Q, and in the same right cell if and only if their images have the same tableau P. In (Shi 1986), Jian-Yi Shi showed that left cells for S ~ ~ n are indexed instead by tabloids, and in (Shi 1991) he gave an algorithm to compute the tabloid analogous to the tableau P for an affine permutation. In (Chmutov, Pylyavskyy & Yudovina 2018), the authors extended Shi's work to give a bijective map between S ~ ~ n and triples ( P , Q , ρ ρ ) consisting of two tabloids of the same shape and an integer vector whose entries satisfy certain inequalities. Their procedure uses the matrix representation of affine permutations and generalizes the shadow construction, introduced in (Viennot 1977).