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The Combinatorial Laplacian of the Tutte Complex

✍ Scribed by Graham Denham

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 134 KB
Volume: 242
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8797

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✦ Synopsis

Let M be an ordered matroid and C •• M be an exterior algebra over its underlying set E, graded by both corank and nullity. Then C •0 M is the simplicial chain complex of IN M , the simplicial complex whose simplices are indexed by the independent sets of the matroid. Dually, C 0• M is the cochain complex of IN M * . We give a combinatorial description of a basis of eigenvectors for the combinatorial Laplacian of a family of boundary maps on the double complex, extending work by W.

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