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The title of the article is often translated into English as "Arrays and the combinatorics of Young tableaux". I couldn't find it online, but you might look at this paper arxiv.org/abs/math/0504299, which has a very brief (two page) summary of the main notions associated with arrays in it and is based on a similar viewpoint as the aforementioned paper.
There is also Silverman and Tate's "Rational Points on Elliptic Curves" which is even more explicit and introduces the subject to undergraduate students.
I guess I abuse language and would call this the Bruhat order. Or I might call it the $Gr(k,n)$-Bruhat order. I think this is what most of the Schubert calculus world would do, but there may be a different name in other contexts.
