... t < k + 2 and k= k + 2 − s, otherwise.If s ranges over 1, 2, . . . , k + 1 and t ranges over s, s + 1, . . . , k + 1 for the first case and sranges over 1, 2, . . . , k + 2 and t = k + ... T2n), whereπiis a matching and Tiis a standard Young tableau (SYT). Let π0be the empty matching and T0be the empty SYT. The tableau Tiis obtained from Ti−1 and the matching πiisobtained ... M´edicis and Viennot [25], de Sainte-Catherine [28], Gessel and Viennot [16], Gouyou-Beauchamps [18, 19], Stein [33], Touchard [36], and recently byKlazar [21, 22, 23], Chen, Deng, Du, Stanley and...