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.
References:
[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 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, svn://svn.macaulay2.com/Macaulay2/trunk/M2/Macaulay2/packages/SimplicialDecomposability.m2, release number 11861.
This documentation describes version 1.0.6 of SimplicialDecomposability.
The source code from which this documentation is derived is in the file SimplicialDecomposability.m2.