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