Abstract
It is proved that the fundamental groups of boolean representable simplicial complexes (BRSC) are free and the rank is determined by the number and nature of the connected components of their graph of flats for dimension ≥ 2. In the case of dimension 2, it is shown that BRSC have the homotopy type of a wedge of spheres of dimensions 1 and 2. Also, in the case of dimension 2, necessary and sufficient conditions for shellability and being sequentially Cohen-Macaulay are determined. Complexity bounds are provided for all the algorithms involved.
| Original language | English |
|---|---|
| Pages (from-to) | 121-156 |
| Number of pages | 36 |
| Journal | International Journal of Algebra and Computation |
| Volume | 27 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Feb 2017 |
Bibliographical note
Publisher Copyright:© 2017 World Scientific Publishing Company.
Keywords
- EL-labeling
- Simplicial complex
- boolean representation
- fundamental group
- homotopy type
- matroid
- sequentially Cohen-Macaulay
- shellability