8 papers
A Uniform Sampling Procedure for Abstract Triangulations of Surfaces
Rajan Shankar, Jonathan Spreer
We present a procedure to sample uniformly from the set of combinatorial isomorphism types of balanced triangulations of surfaces - also known as graph-encoded surfaces. For a give…
Hard Diagrams of the Unknot
Benjamin A. Burton, Hsien-Chih Chang, Maarten Löffler +5
We present three "hard" diagrams of the unknot. They require (at least) three extra crossings before they can be simplified to the trivial unknot diagram via Reidemeister moves in…
Parametrized Complexity of Expansion Height
Ulrich Bauer, Abhishek Rathod, Jonathan Spreer
Deciding whether two simplicial complexes are homotopy equivalent is a fundamental problem in topology, which is famously undecidable. There exists a combinatorial refinement of th…
Combinatorial Inscribability Obstructions for Higher-Dimensional Polytopes
Joseph Doolittle, Jean-Philippe Labbé, Carsten E. M. C. Lange +3
For -dimensional convex polytopes, inscribability is a classical property that is relatively well-understood due to its relation with Delaunay subdivisions of the plane and hype…
3-Manifold triangulations with small treewidth
Kristóf Huszár, Jonathan Spreer
Motivated by fixed-parameter tractable (FPT) problems in computational topology, we consider the treewidth of a compact, connected 3-manifold defined by \[ \operatorname{tw}(M)…
Average Betti numbers of induced subcomplexes in triangulations of manifolds
Giulia Codenotti, Francisco Santos, Jonathan Spreer
We study a variation of Bagchi and Datta's -vector of a simplicial complex , whose entries are defined as weighted averages of Betti numbers of induced subcomplexes of . W…