Rota's Conjecture and Positivity of Algebraic Cycles in Permutohedral Varieties.
Year: 2014
Type: dissertation
Abstract: 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.
Author: June Huh
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4300574146