Tropical Ideals

Diane Maclagan (1) , Felipe Rincón (2)

1 WMI - Warwick Mathematics Institute
2 UiO - University of Oslo

We introduce and study a special class of ideals over the semiring of tropical polynomials, which we calltropical ideals, with the goal of developing a useful and solid algebraic foundation for tropical geometry. We exploretheir rich combinatorial structure, and prove that they satisfy numerous properties analogous to classical ideals.

Domaines: Combinatoire [math.CO]

Diane Maclagan, Felipe Rincón. Tropical Ideals. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6358⟩. ⟨hal-02168123⟩