Hodge Theory for Combinatorial Geometries
نویسندگان
چکیده
The matroid is called loopless if the empty subset of E is closed, and is called a combinatorial geometry if in addition all single element subsets of E are closed. A closed subset of E is called a flat of M, and every subset of E has a well-defined rank and corank in the poset of all flats of M. The notion of matroid played a fundamental role in graph theory, coding theory, combinatorial optimization, and mathematical logic; we refer to [Wel71] and [Oxl11] for general introduction. As a generalization of the chromatic polynomial of a graph [Bir12, Whi32], Rota defined for an arbitrary matroid M the characteristic polynomial
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