Martin Winter

activity

20182023

most citedGeometry and Topology of Symmetric Point Arrangements

2 citations · 7 across the 13 of their papers we have counts for

collaborators

14 papers

math.CO2023

Kalai's $3^{d}$ conjecture for unconditional and locally anti-blocking polytopes

Raman Sanyal, Martin Winter

Kalai's $3^{d}$ conjecture states that every centrally-symmetric $d$ -polytope has at least $3^{d}$ faces. We give short proofs for two special cases: if $P$ is unconditional (that is,…

math.CO2023

The clique graphs of the hexagonal lattice -- an explicit construction and a short proof of divergence

Martin Winter

We present a new, explicit and very geometric construction for the iterated clique graphs of the hexagonal lattice $Hex$ which makes apparent its clique-divergence and she…

math.CO2023

Characterising Clique Convergence for Locally Cyclic Graphs of Minimum Degree $δ \geq 6$

Anna M. Limbach, Martin Winter

The clique graph $k G$ of a graph $G$ has as its vertices the cliques (maximal complete subgraphs) of $G$ , two of which are adjacent in $k G$ if they have non-empty intersection in $…

math.CO2023

Rigidity, Tensegrity and Reconstruction of Polytopes under Metric Constraints

Martin Winter

We conjecture that a convex polytope is uniquely determined up to isometry by its edge-graph, edge lengths and the collection of distances of its vertices to some arbitrary interio…

math.CO2022

(Random) Trees of Intermediate Uniform Growth

George Kontogeorgiou, Martin Winter

For every sufficiently well-behaved function $g : R_{\geq 0} \to R_{\geq 0}$ that grows at least linearly and at most exponentially we construct a tree $T$ of u…

cs.LG2022

Gradient-based Weight Density Balancing for Robust Dynamic Sparse Training

Mathias Parger, Alexander Ertl, Paul Eibensteiner +3

Training a sparse neural network from scratch requires optimizing connections at the same time as the weights themselves. Typically, the weights are redistributed after a predefine…

math.MG2021★ 2 cited

Capturing Polytopal Symmetries by Coloring the Edge-Graph

Martin Winter

A general (convex) polytope $P \subset R^{d}$ and its edge-graph $G_{P}$ can have very distinct symmetry properties. We construct a coloring (of the vertices and edges) of the ed…

math.MG2020★ 1 cited

Eigenpolytopes, Spectral Polytopes and Edge-Transitivity

Martin Winter

Starting from a finite simple graph $G$ , for each eigenvalue $θ$ of its adjacency matrix one can construct a convex polytope $P_{G} (θ)$ , the so called $θ$ -eigenpolytop of $G$ . For so…

math.CO2020★ 2 cited

Symmetric and Spectral Realizations of Highly Symmetric Graphs

Martin Winter

A realization of a graph $G = (V, E)$ is a map $v : V \to R^{d}$ that assigns to each vertex a point in $d$ -dimensional Euclidean space. We study graph realizations from the pers…

math.MG2020

The Edge-transitive Polytopes that are not Vertex-transitive

Frank Göring, Martin Winter

In 3-dimensional Euclidean space there exist two exceptional polyhedra, the rhombic dodecahedron and the rhombic triacontahedron, the only known polytopes (besides polygons) that a…

math.MG2019

Classification of Vertex-Transitive Zonotopes

Martin Winter

We give a full classification of vertex-transitive zonotopes. We prove that a vertex-transitive zonotope is a $Γ$ -permutahedron for some finite reflection group $Γ\subset\mathrm{O}…

math.MG2019★ 2 cited

Geometry and Topology of Symmetric Point Arrangements

Martin Winter

We investigate point arrangements $v_{i} \in R^{d}, i \in {1, ..., n}$ with certain prescribed symmetries. The arrangement space of $v$ is the column span of the matrix in which t…

math.CO2018

Vertex-Facet Assignments For Polytopes

Thomas Jahn, Martin Winter

Motivated by the search for reduced polytopes, we consider the following question: For which polytopes exists a vertex-facet assignment, that is, a matching between vertices and no…

cs.GR2018

AlSub: Fully Parallel and Modular Subdivision

Daniel Mlakar, Martin Winter, Hans-Peter Seidel +2

In recent years, mesh subdivision---the process of forging smooth free-form surfaces from coarse polygonal meshes---has become an indispensable production instrument. Although subd…

Kalai's 3d conjecture for unconditional and locally anti-blocking polytopes

The clique graphs of the hexagonal lattice -- an explicit construction and a short proof of divergence

Characterising Clique Convergence for Locally Cyclic Graphs of Minimum Degree δ≥6

Rigidity, Tensegrity and Reconstruction of Polytopes under Metric Constraints

(Random) Trees of Intermediate Uniform Growth

Gradient-based Weight Density Balancing for Robust Dynamic Sparse Training

Capturing Polytopal Symmetries by Coloring the Edge-Graph

Eigenpolytopes, Spectral Polytopes and Edge-Transitivity

Symmetric and Spectral Realizations of Highly Symmetric Graphs

The Edge-transitive Polytopes that are not Vertex-transitive

Classification of Vertex-Transitive Zonotopes

Geometry and Topology of Symmetric Point Arrangements

Vertex-Facet Assignments For Polytopes

AlSub: Fully Parallel and Modular Subdivision

Kalai's $3^{d}$ conjecture for unconditional and locally anti-blocking polytopes

Characterising Clique Convergence for Locally Cyclic Graphs of Minimum Degree $δ \geq 6$