NDLI: Homology of the boolean complex

Content Provider	Springer Nature Link
Author	Ragnarsson, Kári Tenner, Bridget Eileen
Copyright Year	2011
Abstract	We construct and analyze an explicit basis for the homology of the boolean complex of a finite simple graph. This provides a combinatorial description of the spheres in the wedge sum representing the homotopy type of the complex. We assign a set of derangements to any finite simple graph. For each derangement, we construct a corresponding element in the homology of the complex, and the collection of these elements forms a basis for the homology of the boolean complex. In this manner, the spheres in the wedge sum describing the homotopy type of the complex can be represented by a set of derangements.We give an explicit, closed-form description of the derangements that can be obtained from any finite simple graph, and compute this set for several families of graphs. In the cases of complete graphs and Ferrers graphs, these calculations give bijective proofs of previously obtained enumerative results.
Starting Page	617
Ending Page	639
Page Count	23
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	34
Issue Number	4
e-ISSN	15729192
Language	English
Publisher	Springer US
Publisher Date	2011-04-21
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Coxeter system Boolean complex Homology Derangement Complete graph Ferrers graph Staircase shape Group Theory and Generalizations Computer Science Order, Lattices, Ordered Algebraic Structures Convex and Discrete Geometry Combinatorics
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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