Stack words, standard tableaux and Baxter permutations

Abstract The origin of this work is based on the enumeration of stack sortable permutations [11, 17, 18]. The problem, particularly in case of two stacks, exhibits classical objects in combinatorics such as permutations with forbidden subsequences, nonseparable planar maps [4, 5], and also standard Young tableaux if we are interested in the movements of stacks. So, we show that the number of 3 × n rectangular standard Young tableaux which avoid two consecutive integers on second row is c2n (where cn = (2n)!/(n + 1)!n!) and there is a one-to-one correspondence between the same tableaux which avoid two consecutive integers on the same row and Baxter permutations which are enumerated by . We also give formulas enumerating these objects according to various parameters.