Method to rank and unrank semi-standard Young tableau for a partition of n

Abstract

The semi-standard Young tableau (SSYT), on k-symbols are one type of combinatorial objects, which have one-to-one correspondence with Gelfand–Tzetlin bases set of the unitary group U(k) and hence are adapted to the chain of subgroups U(k) ⊂ U (k − 1) ⊂ · · ·U(1). In the present work, we use this result and the general framework suggested by Wilf [Wilf, H. S. (1977). A unified setting for sequencing, ranking and selection algorithms for combinatorial objects. Adv. Math., 24, 281–291.] to rank and unrank SSYTs.