Stack words, standard Young tableaux, permutations with forbidden subsequences and planar maps

Abstract

Stack words stem from studies on stack-sortable permutations and represent classical combinatorial objects such as standard Young tableaux, permutations with forbidden sequences and planar maps. We extend existing enumerative results on stack words and we also obtain new results. In particular, we make a correspondence between nonseparable 3× n rectangular standard Young tableaux (or stack words where elements satisfy a ‘Towers of Hanoi’ condition) and nonseparable cubic rooted planar maps with 2 n vertices enumerated by 2 n (3 n)!/((2 n+1)!( n+1)!). Moreover, these tableaux without two consecutive integers in the same row are in bijection with nonseparable rooted planar maps with n+1 edges enumerated by 2(3 n)!/((2 n+1)!( n+1)!).