Tropical Division and FactorizaTion of Generalized Permutahedra
PREPRINT
I use Tropical Geometry to give criteria for the existence of a factorization of tropical polynomial functions and use this to study the decomposition of generalized permutahedra and Coxeter polytopes as signed and weighted Minkowski sums.
ARXIV.ORG/ABS/1908.00241
I use Tropical Geometry to give criteria for the existence of a factorization of tropical polynomial functions and use this to study the decomposition of generalized permutahedra and Coxeter polytopes as signed and weighted Minkowski sums.
ARXIV.ORG/ABS/1908.00241
Tropical Geometry and Mechanism Design
PREPRINT
Joint work with Ngoc Tran. We apply Tropical Geometry to Mechanism Design. In this paper we build on a network theoretic approach and derive a fully geometric and algebraic theory of dominant strategy implementation.
ARXIV.ORG/ABS/1606.04880
BLOG POST
For a leisurely overview of the broad ideas using Tropical Geometry in Mechanism Design without too many technical details you may enjoy reading the following blog post on Ngoc Tran's Blog.
Joint work with Ngoc Tran. We apply Tropical Geometry to Mechanism Design. In this paper we build on a network theoretic approach and derive a fully geometric and algebraic theory of dominant strategy implementation.
ARXIV.ORG/ABS/1606.04880
BLOG POST
For a leisurely overview of the broad ideas using Tropical Geometry in Mechanism Design without too many technical details you may enjoy reading the following blog post on Ngoc Tran's Blog.