Rota’s conjecture predicts that the coefficients of the characteristic polynomial of a matroid form a log-concave sequence. I will outline a proof for representable matroids using Milnor numbers and the Bergman fan. The same approach to the conjecture in the general case (for possibly non-representable matroids) leads to several intriguing questions on higher codimension algebraic cycles in toric varieties.
CITATION STYLE
Huh, J. (2015). Rota’s conjecture, the missing axiom, and prime cycles in toric varieties. In Springer INdAM Series (Vol. 12, pp. 59–62). Springer International Publishing. https://doi.org/10.1007/978-3-319-20155-9_12
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