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.
|Original language||English (US)|
|Title of host publication||Springer INdAM Series|
|Publisher||Springer International Publishing|
|Number of pages||4|
|State||Published - 2015|
|Name||Springer INdAM Series|
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