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- Title
The first cotangent cohomology module for matroids.
- Authors
Brehm, William; Constantinescu, Alexandru
- Abstract
We find a combinatorial formula which computes the first cotangent cohomology module of Stanley–Reisner rings associated to matroids. For arbitrary simplicial complexes we provide upper bounds for the dimensions of the multigraded components of T¹ . For specific degrees we prove that these bounds are reached if and only if the simplicial complex is a matroid, obtaining thus a new characterization for matroids. Furthermore, the graded first cotangent cohomology turns out to be a complete invariant for nondiscrete matroids.
- Subjects
COHOMOLOGY theory; MATROIDS; COMBINATORICS; MATHEMATICAL bounds; INVARIANTS (Mathematics)
- Publication
Journal of Combinatorial Algebra, 2023, Vol 7, Issue 2, p327
- ISSN
2415-6302
- Publication type
Article
- DOI
10.4171/JCA/73