Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On lexicographically shellable posets


Authors: Anders Björner and Michelle Wachs
Journal: Trans. Amer. Math. Soc. 277 (1983), 323-341
MSC: Primary 06A10; Secondary 05A99, 52A25, 57Q05
DOI: https://doi.org/10.1090/S0002-9947-1983-0690055-6
MathSciNet review: 690055
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Lexicographically shellable partially ordered sets are studied. A new recursive formulation of $ {\text{CL}}$-shellability is introduced and exploited. It is shown that face lattices of convex polytopes, totally semimodular posets, posets of injective and normal words and lattices of bilinear forms are $ {\text{CL}}$-shellable. Finally, it is shown that several common operations on graded posets preserve shellability and $ {\text{CL}}$-shellability.


References [Enhancements On Off] (What's this?)

  • [1] A. Björner, Shellable and Cohen-Macaulay partially ordered sets, Trans. Amer. Math. Soc. 260 (1980), 159-183. MR 570784 (81i:06001)
  • [2] A. Björner and M. Wachs, Bruhat order of Coxeter groups and shellability, Adv. in Math. 43 (1982), 87-100. MR 644668 (83i:20043)
  • [3] H. Bruggesser and P. Mani, Shellable decompositions of cells and spheres, Math. Scand. 29 (1971), 197-205. MR 0328944 (48:7286)
  • [4] P. J. Cameron and M. Deza, On permutation geometries, J. London Math. Soc. (2) 20 (1979), 373-386. MR 561129 (81i:05049)
  • [5] G. Danaraj and V. Klee, Shellings of spheres and polytopes, Duke Math. J. 41 (1974), 443-451. MR 0345113 (49:9852)
  • [6] P. Delsarte, Association schemes and $ t$-designs in regular semilattices, J. Combin. Theory Ser. A 20 (1976), 230-243. MR 0401512 (53:5339)
  • [7] F. D. Farmer, Cellular homology for posets, Math. Japon. 23 (1979), 607-613. MR 529895 (82k:18013)
  • [8] R. P. Stanley, Balanced Cohen-Macaulay complexes, Trans. Amer. Math. Soc. 249 (1979), 139-157. MR 526314 (81c:05012)
  • [9] D. Stanton, A partially ordered set and $ q$-Krawtchouk polynomials, J. Combin. Theory Ser. A 30 (1981), 276-284. MR 618532 (83d:05027)
  • [10] D.-N. Verma, Möbius inversion for the Bruhat ordering on a Weyl group, Ann. Sci. École Norm. Sup. 4 (1971), 393-398. MR 0291045 (45:139)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 06A10, 05A99, 52A25, 57Q05

Retrieve articles in all journals with MSC: 06A10, 05A99, 52A25, 57Q05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0690055-6
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society