Catalan Triangle, Standard Young Words and Standard Young Tableaux

Abstract

In this paper, we introduce a new sequence called standard Young words, which are defined as quaternary words with interesting restrictions. First, we show that the cardinality of standard Young words of length n is related to Catalan triangle sequence and we establish a bijection from the set of standard Young words to the set of pairs of non-intersection lattice paths. Then we set a one-to-one correspondence between the set of standard Young words and the set of standard Young tableaux of two rows, which results in the correspondence between the statistics of standard Young words and standard Young tableaux, such as sign and descents.