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SimplicialDecomposability :: SimplicialDecomposability

SimplicialDecomposability -- various decomposability routines for simplicial complexes.


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.


Certification a gold star

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://, release number 11861.


This documentation describes version 1.0.6 of SimplicialDecomposability.

Source code

The source code from which this documentation is derived is in the file SimplicialDecomposability.m2.


  • Functions and commands
    • allFaces -- returns all faces of a simplicial complex, up to a given dimension
    • faceDelete -- computes the face deletion for a simplicial complex
    • fTriangle -- determines the f-Triangle of a simplicial complex
    • hTriangle -- determines the h-Triangle of a simplicial complex
    • hVector -- determines the h-Vector of a simplicial complex
    • isDecomposable -- determines whether a simplicial complex is k-decomposable
    • isSheddingFace -- determines whether a face of a simplicial complex is a shedding face
    • isSheddingVertex -- determines whether a vertex of a simplicial complex is a shedding vertex
    • isShellable -- determines whether a simplicial complex is shellable
    • isShelling -- determines whether a list of faces is a shelling
    • isSimplex -- determines whether a simplicial complex is simplex
    • isVertexDecomposable -- determines whether a simplicial complex is vertex-decomposable
    • shellingOrder -- finds a shelling of a simplicial complex, if one exists
  • Symbols