2013/02/13 by Eu, Sen-Peng, Fu, Tung-Shan, Hou, Justin T. +1 · 1 citation
#05A15 #05A19 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1302.3012
In this paper, we propose a notion of colored Motzkin paths and establish a bijection between the n-cell standard Young tableaux (SYT) of bounded height and the colored Motzkin paths of length n. This result not only gives a lattice path interpretation of the standard Young tableaux but also reveals an unexpected intrinsic relation between the set of SYTs with at most 2d+1 rows and the set of SYTs with at most 2d rows.