Combinatorial correspondences for Young tableaux, balanced tableaux, and maximal chains in the weak Bruhat order of \(S_ n\). (English) Zbl 0562.05008

Edelman, Paul; Greene, Curtis

Combinatorics and algebra, Proc. Conf., Boulder/Colo. 1983, Contemp. Math. 34, 155-162 (1984).

[For the entire collection see Zbl 0546.00008.]
R. Stanley proved that the number of maximal chains in the weak Bruhat order of \(S_ n\) is equal to the number of Young tableaux of staircase shape. In this note Stanley’s result is proved by direct combinatorial correspondences. A number of further informations relating tableaux to chains in the weak Bruhat order are given.

Reviewer: J.Cigler

MSC:

05A17

Combinatorial aspects of partitions of integers

Keywords:

maximal chains; weak Bruhat order; Young tableaux