Moduli space of families of positive $(n-1)$-weights

TL;DR

This paper explores the geometric structure of the moduli space of positive-weighted trees with labeled leaves, characterizing families of positive multi-weights that realize the same set of positive $(n-1)$-weights.

Contribution

It provides a geometric description of the moduli space of positive-weighted trees with fixed positive $(n-1)$-weights, linking them to positive multi-weights.

Findings

Characterization of the moduli space structure.

Identification of conditions for trees to realize the same weights.

Connection between positive weights and multi-weights.

Abstract

We show the geometrical structure of the moduli space of positive-weighted trees with $n$ labels $1,\ldots , n$ which realize the same family of positive $(n-1)$-weights and we characterize them as a family of positive multi-weights.