This package includes routines for vertex decomposability and shellability for arbitrary simplicial complexes as well as routines for k-decomposability. Moreover, it can find a shelling order for a shellable simplicial complex.
[BW-1] A. Bjoerner and M. Wachs, "Shellable nonpure complexes and posets, I," Trans. of the AMS 348 (1996), 1299–1327.
[BW-2] A. Bjoerner and M. Wachs, "Shellable nonpure complexes and posets, II," Trans. of the AMS 349 (1997), 3945–3975.
[MT] S. Moriyama and F. Takeuchi, "Incremental construction properties in dimension two: shellability, extendable shellability and vertex decomposability," Discrete Math. 263 (2003), 295–296.
[PB] J. S. Provan and L. J. Billera, "Decompositions of Simplicial Complexes Related to Diameters of Convex Polyhedra," Math. of Operations Research 5 (1980), 576–594.
[St] R. Stanley, "Combinatorics and Commutative Algebra," 2nd edition. Progress in Mathematics, 41. Birkhaeuser Boston, Inc. Boston, MA, 1996.
[Wo] R. Woodroofe, "Chordal and sequentially Cohen-Macaulay clutters," arXiv:0911.4697v1.
Version 1.0.5 of this package was accepted for publication in volume 2 of The Journal of Software for Algebra and Geometry: Macaulay2 on 2010-08-03, in the article Simplicial Decomposability. That version can be obtained from the journal or from the Macaulay2 source code repository.
This documentation describes version 1.0.6 of SimplicialDecomposability.
The source code from which this documentation is derived is in the file SimplicialDecomposability.m2.