Generalized permutahedra and positive flag Dressians
Michael Joswig, Georg Loho, Dante Luber, Jorge Alberto Olarte
TL;DR
This paper explores the structure of valuated matroids, flag matroids, and their relation to permutahedral subdivisions, providing new characterizations of positive flag Dressians and their geometric properties.
Contribution
It introduces a novel characterization of permutahedral subdivisions and positive valuated flag matroids, linking tropical geometry with total positivity.
Findings
Characterization of permutahedral subdivisions into generalized permutahedra
Identification of subdivisions arising from positive valuated flag matroids
Connections between tropical incidence relations and total positivity
Abstract
We study valuated matroids, their tropical incidence relations, flag matroids and total positivity. This leads to a characterization of permutahedral subdivisions, namely subdivisions of regular permutahedra into generalized permutahedra. Further, we get a characterization of those subdivisions arising from positive valuated flag matroids.
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