arXiv subjects

Lena Weis

Publications and source records attributed to Lena Weis.

2 recordsLinked to original sources

arXiv2026

Tropical $k$-means clustering for phylogenetic trees

The asymmetric tropical distance is a distance measure on the tropical torus $\mathbb{R}^n/\mathbb{R}\mathbf{1}$ and in particular on the Bergman fan $B(K_N) \subseteq \mathbb{R}^{\binom{N}{2}}/\mathbb{R}\mathbf{1}$ of the complete graphical matroid. In this paper, we define and analyse a clustering algorithm for equidistant phylogenetic trees based on this distance, using the correspondence between $B(K_N)$ and the space of equidistant trees with $N$ leaves.

math.CO↗

arXiv2025

Shellings of Unbounded Polyhedra

The shellability of the boundary complex of an unbounded polyhedron is investigated. To this end, it is necessary to study suitable compactifications first. Results on polyhedra can then be exploited to derive a shellability result for tropical hypersurfaces. Under the hood there is a subtle interplay between the duality of polyhedral complexes and their shellability. Translated into discrete Morse theory, that interplay also gives that the tight span of a regular subdivision is collapsible, but not shellable in general.

math.CO↗