Estimation of the number of permutationally-ordered sets / *M. I. Kharitonov.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 3. P. 24-28
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 125-129].

It is proved that the number of *n*-element permutationally-ordered sets with the
maximal antichain of length not exceeding *k* is not greater than
*k* satisfies the inequality

*Key words*:
combinatorics on words, *k*-divisibility, Dilworth theorem, multilinear words, multilinear identities, Young diagrams.