Rota's Conjecture and Positivity of Algebraic Cycles in Permutohedral Varieties.

Algebraic Cycles;Positivity;Mathematics;Science;Mathematics

Huh, JuneFomin, Sergey ;

University of Michigan

关键词: Algebraic Cycles;    Positivity;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/108901/junehuh_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Rota;;s conjecture predicts that the coefficients of the characteristic polynomial of a matroid form a log-concave sequence. We give a proof of the conjecture for realizable matroids using techniques of algebraic geometry. The same approach to the conjecture in the general case (for possibly non-realizable matroids) leads to several intriguing questions on higher codimension algebraic cycles in the toric variety associated to the permutohedron.