2 research outputs found
Multivariate volume, Ehrhart, and -polynomials of polytropes
The univariate Ehrhart and -polynomials of lattice polytopes have been
widely studied. We describe methods from toric geometry for computing
multivariate versions of volume, Ehrhart and -polynomials of lattice
polytropes, which are both tropically and classically convex. These algorithms
are applied to all polytropes of dimensions 2,3 and 4, yielding a large class
of integer polynomials. We give a complete combinatorial description of the
coefficients of volume polynomials of 3-dimensional polytropes in terms of
regular central subdivisions of the fundamental polytope. Finally, we provide a
partial characterization of the analogous coefficients in dimension 4.Comment: 19 page
Tropical pseudolinear and pseudoquadratic optimization as parametric mean-payoff games
We apply an approach based on parametric mean-payoff games to develop
bisection and Newton schemes for solving problems of tropical pseudolinear and
pseudoquadratic optimisation with general two-sided constraints.Comment: 30 pages (with appendices), 9 figure