Abstract
The enumeration of standard Young tableaux (SYTs) is a fundamental problem in combinatorics and representation theory. While counting SYTs of bounded height k is known for k at most 5 with combinatorial proofs, much less is known for counting SYTs in a (k,l)-hook. In 2009 Regev enumerated standard Young tableaux of order n that are contained in a (2,1)-hook. By a recurrence relation and the WZ method he proved that this number is 12(∑j≥1njn−jj)+1. In this paper we give a combinatorial proof of Regev’s result by constructing a bijection between these tableaux and free Motzkin paths.
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