Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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The Bruhat order of the symmetric group is lexicographically shellable
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by Paul H. Edelman
Proc. Amer. Math. Soc. 82 (1981), 355-358
DOI: https://doi.org/10.1090/S0002-9939-1981-0612718-4

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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Bibliographic Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 82 (1981), 355-358
  • MSC: Primary 06A10; Secondary 13H10, 14M05, 20B99, 52A22
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0612718-4
  • MathSciNet review: 612718