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Hodge theory of matroids by star subdivisions
Andy Hsiao
https://arxiv.org/abs/2509.10909 https://arxiv.org/pdf/2509.10909…

Hodge theory of matroids by star subdivisions
It is known that the Chow ring of a matroid satisfies the Hard Lefschetz property and Hodge Riemann relations. We provide a proof of this theorem by decomposition of the deletion operation into star subdivisions at two dimensional cones. This gives a simple combinatorial proof which avoids intersection cohomology or algebraic geometry.

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