On lexicographically shellable posets

Björner, Anders; Wachs, Michelle

doi:10.1090/S0002-9947-1983-0690055-6

On lexicographically shellable posets
HTML articles powered by AMS MathViewer

by Anders Björner and Michelle Wachs PDF

Trans. Amer. Math. Soc. 277 (1983), 323-341 Request permission

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

Anders Björner, Shellable and Cohen-Macaulay partially ordered sets, Trans. Amer. Math. Soc. 260 (1980), no. 1, 159–183. MR 570784, DOI 10.1090/S0002-9947-1980-0570784-2
Anders Björner and Michelle Wachs, Bruhat order of Coxeter groups and shellability, Adv. in Math. 43 (1982), no. 1, 87–100. MR 644668, DOI 10.1016/0001-8708(82)90029-9
H. Bruggesser and P. Mani, Shellable decompositions of cells and spheres, Math. Scand. 29 (1971), 197–205 (1972). MR 328944, DOI 10.7146/math.scand.a-11045
P. J. Cameron and M. Deza, On permutation geometries, J. London Math. Soc. (2) 20 (1979), no. 3, 373–386. MR 561129, DOI 10.1112/jlms/s2-20.3.373
Gopal Danaraj and Victor Klee, Shellings of spheres and polytopes, Duke Math. J. 41 (1974), 443–451. MR 345113
Philippe Delsarte, Association schemes and $t$-designs in regular semilattices, J. Combinatorial Theory Ser. A 20 (1976), no. 2, 230–243. MR 401512, DOI 10.1016/0097-3165(76)90017-0
Frank D. Farmer, Cellular homology for posets, Math. Japon. 23 (1978/79), no. 6, 607–613. MR 529895
Richard P. Stanley, Balanced Cohen-Macaulay complexes, Trans. Amer. Math. Soc. 249 (1979), no. 1, 139–157. MR 526314, DOI 10.1090/S0002-9947-1979-0526314-6
Dennis Stanton, A partially ordered set and $q$-Krawtchouk polynomials, J. Combin. Theory Ser. A 30 (1981), no. 3, 276–284. MR 618532, DOI 10.1016/0097-3165(81)90023-6
Daya-Nand Verma, Möbius inversion for the Bruhat ordering on a Weyl group, Ann. Sci. École Norm. Sup. (4) 4 (1971), 393–398. MR 291045, DOI 10.24033/asens.1215