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arXiv · 2210.06868

Generalized metric tree arrangements and Dressians

Ayush Kumar Tewari
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Abstract

Metric trees and metric tree arrangements index cones in the polyhedral fan structure in the Dressian $Dr(2,n)$ and $Dr(3,n)$ respectively. We introduce the notion of generalized metric tree arrangements which parameterize points in $Dr(k,n)$ and extend previously known results to $Dr(k,n)$ along with providing explicit examples of these generalized metric tree arrangements. We study the adjacency of cones in the positive Dressian $Dr_{>0}(3, n)$ and introduce generalized Whitehead moves which provide a condition for adjacency of maximal cones in $Dr_{>0}(3,n)$ in terms of the associated metric tree arrangements.

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Ayush Kumar Tewari. 2022-10-13. Generalized metric tree arrangements and Dressians. https://arxiv.org/abs/2210.06868

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