Painted Tropical Complexes
Gabriel Kerr, Sophia Palcic

TL;DR
This paper introduces painted tropical complexes, establishes a poset structure on them, and demonstrates that multiplihedra are special cases of secondary polytopes, linking tropical geometry with polytope theory.
Contribution
It defines painted tropical complexes, describes their poset structure, and proves that multiplihedra are secondary polytopes, connecting tropical geometry with polytope combinatorics.
Findings
Poset structure on painted tropical complexes
Equivalence of this poset to face lattice of a secondary polytope
Multiplihedra are shown to be secondary polytopes
Abstract
We define the notion of a painted tropical -complex and describe a poset structure on the set of all such complexes. This poset is equivalent to the face lattice of a secondary polytope where is built from and an additional point . As a central application, we show that multiplihedra are also secondary polytopes.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Advanced Combinatorial Mathematics · Polynomial and algebraic computation
