The focus of this report will be on independence complexes constructed from independent sets of members of sequences graphs. For such independence complexes, we will study generating functions and closed formulae for the Euler characteristics and f-polynomials, as well as homology groups of different degrees. All of these can be computed by hand, although this quickly becomes tedious as well as really difficult to do, hence recursive methods will be used instead. the generating functions, bounded formulae and recursive equations will be compared to known number sequences, and where possible bijections to other problems will be establised. For the independence complexes of each graphs sequence, formulae will be given for where the homology groups are nonzero, as well as in some cases formulae for the exact dimensions of the homology groups for each complex.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kth-38265 |
| Date | January 2011 |
| Creators | Fors, Rickard |
| Publisher | KTH, Skolan för datavetenskap och kommunikation (CSC), KTH, Matematik (Inst.) |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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