Results 1 to 10 of about 38 (37)
The equivariant topology of stable Kneser graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Schrijver introduced the stable Kneser graph $SG_{n,k}, n \geq 1, k \geq 0$. This graph is a vertex critical graph with chromatic number $k+2$, its vertices are certain subsets of a set of cardinality $m=2n+k$.
Carsten Schultz
doaj +1 more source
Patchworking oriented matroids
Journal of the London Mathematical Society, Volume 106, Issue 4, Page 3545-3576, December 2022., 2022 Abstract In a previous work, we gave a construction of (not necessarily realisable) oriented matroids from a triangulation of a product of two simplices. In this follow‐up paper, we use a combinatorial analogue of Viro's patchworking to derive a topological representation of the oriented matroid directly from the polyhedral structure of the ...
Marcel Celaya, Georg Loho, Chi Ho Yuen
wiley +1 more source
Modeling Complex Systems by Structural Invariants Approach
Complexity, Volume 2021, Issue 1, 2021., 2021 When modeling complex systems, we usually encounter the following difficulties: partiality, large amount of data, and uncertainty of conclusions. It can be said that none of the known approaches solves these difficulties perfectly, especially in cases where we expect emergences in the complex system.
Jiri Bila +3 more
wiley +1 more source
A Rabbit Hole between Topology and Geometry
International Scholarly Research Notices, Volume 2013, Issue 1, 2013., 2013 Topology and geometry should be very closely related mathematical subjects dealing with space. However, they deal with different aspects, the first with properties preserved under deformations, and the second with more linear or rigid aspects, properties invariant under translations, rotations, or projections.
David G. Glynn +5 more
wiley +1 more source
A tropical approach to rigidity: Counting realisations of frameworks
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract A realisation of a graph in the plane as a bar‐joint framework is rigid if there are finitely many other realisations, up to isometries, with the same edge lengths. Each of these finitely many realisations can be seen as a solution to a system of quadratic equations prescribing the distances between pairs of points.
Oliver Clarke +6 more
wiley +1 more source
Canonical forms of oriented matroids
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract Positive geometries are semialgebraic sets equipped with a canonical differential form whose residues mirror the boundary structure of the geometry. Every full‐dimensional projective polytope is a positive geometry. Motivated by the canonical forms of polytopes, we construct a canonical form for any tope of an oriented matroid inside the Orlik–
Christopher Eur, Thomas Lam
wiley +1 more source
The category of a partitioned fan
Journal of the London Mathematical Society, Volume 111, Issue 2, February 2025.Abstract In this paper the notion of an admissible partition of a simplicial polyhedral fan is introduced and the category of a partitioned fan is defined as a generalisation of the τ$\tau$‐cluster morphism category of a finite‐dimensional algebra. This establishes a complete lattice of categories around the τ$\tau$‐cluster morphism category, which is ...
Maximilian Kaipel
wiley +1 more source
The Poincaré‐extended ab$\mathbf {a}\mathbf {b}$‐index
Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.Abstract Motivated by a conjecture concerning Igusa local zeta functions for intersection posets of hyperplane arrangements, we introduce and study the Poincaré‐extended ab$\mathbf {a}\mathbf {b}$‐index, which generalizes both the ab$\mathbf {a}\mathbf {b}$‐index and the Poincaré polynomial.
Galen Dorpalen‐Barry +2 more
wiley +1 more source
Flip Distances Between Graph Orientations. [PDF]
Algorithmica, 2021 Aichholzer O +6 more
europepmc +1 more source
Knot theory and error-correcting codes. [PDF]
Des Codes CryptogrKılıç AB +3 more
europepmc +1 more source