In combinatorics, the phrase rank of a partition is sometimes used to describe a different concept: the rank of a partition λ is the largest integer i such that λ has at least i parts each of which is no smaller than i.Stanley, Richard P. (1999) Enumerative Combinatorics, Volume 2, p. 289. Cambridge University Press. . Equivalently, this is the length of the main diagonal in the Young diagram or Ferrers diagram for λ, or the side-length of the Durfee square of λ.
