The Bruhat order of the symmetric group is lexicographically shellable

Author:
Paul H. Edelman

Journal:
Proc. Amer. Math. Soc. **82** (1981), 355-358

MSC:
Primary 06A10; Secondary 13H10, 14M05, 20B99, 52A22

MathSciNet review:
612718

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Abstract: The title theorem is proven. It then follows from a theorem of Björner that the simplicial complex of chains of this Bruhat order is shellable and thus Cohen-Macaulay. It is further established that this complex is a double cone over a triangulation of a sphere.

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DOI:
https://doi.org/10.1090/S0002-9939-1981-0612718-4

Article copyright:
© Copyright 1981
American Mathematical Society