Non-Generic Tropical Hyperplane Arrangements and the Secondary polytope of $Δ_{n-1} \times Δ_{d-1}$

Details Non-Generic Tropical Hyperplane Arrangements and the Secondary polytope of $Δ_{n-1} \times Δ_{d-1}$ Non-Generic Tropical Hyperplane Arrangements and the Secondary polytope of $Δ_{n-1} \times Δ_{d-1}$

2010-10-07

arxiv.org/abs/1010.1446v1

Mathematics

Combinatorics

Scientific paper

Ardila and Develin's paper on tropical oriented hyperplane arrangements and tropical oriented matroids defines tropical oriented matroids and conjectures a bijection between them and triangulations of products of simplices $\Delta_{n-1} \times \Delta_{d-1}$. Oh and Yoo recently confirmed this conjecture; however, neither group addressed the case of hyperplanes that are not in generic position. These non-generic arrangements do not correspond to tropical oriented matroids, but they encode information about subdivisions of $\Delta_{n-1} \times \Delta_{d-1}$. This note considers the non-generic case and presents some preliminary results in the area.

Affiliated with

Also associated with

No associations

Rating

Non-Generic Tropical Hyperplane Arrangements and the Secondary polytope of $Δ_{n-1} \times Δ_{d-1}$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Non-Generic Tropical Hyperplane Arrangements and the Secondary polytope of $Δ_{n-1} \times Δ_{d-1}$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non-Generic Tropical Hyperplane Arrangements and the Secondary polytope of $Δ_{n-1} \times Δ_{d-1}$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-509717