| Young tableaux and lattice paths are important combinatorial structures in enumerative combinatorics.Young tableaux are widely used in combinatorial mathematics,Schubert cal-culus and representation theory,and lattice paths are useful in statistics,probability theory,random process and other branches of mathematics.In 2009 Regev enumerated standard Young tableaux of order n that is contained in a（2,1）-hook.By a recurrence relation and the WZ method he proved that this number is 1/2(∑j≥1（jn）(jn-j))+1. In this paper we de-fine“tight”012-words and give a combinatorial proof of Regev’s result by constructing a bijection between these tableaux and super Motzkin paths. |
