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Iterated homology and decompositions of simplicial complexes
| Content Provider | Semantic Scholar |
|---|---|
| Author | Duval, Art M. Zhang, Ping |
| Copyright Year | 2001 |
| Abstract | Kalai has conjectured that a simplicial complex can be partitioned into Boolean algebras at least as roughly, as a shifting-preserving collapse sequence of its algebraically shifted complex. In particular, then, a simplicial complex could (conjecturally) be partitioned into Boolean intervals whose sizes are indexed by its iterated Betti numbers, a generalization of ordinary homology Betti numbers. This would imply a long-standing conjecture made (separately) by Garsia and Stanley concerning partitions of Cohen-Macaulay complexes into Boolean intervals.We prove a relaxation of Kalai’s conjecture, showing that a simplicial complex can be partitioned into recursively defined spanning trees of Boolean intervals indexed by its iterated Betti numbers. |
| Starting Page | 313 |
| Ending Page | 331 |
| Page Count | 19 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/BF02802509 |
| Volume Number | 121 |
| Alternate Webpage(s) | https://gilkalai.files.wordpress.com/2017/02/duval-zhang.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/BF02802509 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
