Related papers: Quaternary matroids are vf-safe
This note contributes to the structure theory of abstract rigidity matroids in general dimension. In the spirit of classical matroid theory, we prove several cryptomorphic characterizations of abstract rigidity matroids (in terms of…
A hypermap is an embedding of a connected hypergraph into an orientable closed surface. A covering between hypermaps is a homomorphism between the embedded hypergraphs which extends to an orientation-preserving covering of the supporting…
It is shown that the group of nonzero quaternions carries a family of natural closed Friedmann-Lema\^{\i}tre-Robertson-Walker metrics.
A biased graph is a graph with a class of selected circles ("cycles", "circuits"), called balanced, such that no theta subgraph contains exactly two balanced circles. A biased graph $\Omega$ has two natural matroids, the frame matroid…
A recent line of research has concentrated on exploring the links between analytic and combinatorial theories of submodularity, uncovering several key connections between them. In this context, Lov\'asz initiated the study of matroids from…
Inspired by a recent result of Brakensiek et al. that symmetric tensor matroids and rigidity matroids are linked by matroid duality, we define abstract symmetric tensor matroids as a dual concept to abstract rigidity matroids and establish…
For billiards with $N$ obstacles on a torus, we study the behavior of specific kind of its trajectories, \emph{the so called admissible trajectories}. Using the methods developed in \cite{1}, we prove that the \emph{admissible rotation set}…
We study the abstract regular polyhedra with automorphism groups that act faithfully on their vertices, and show that each non-flat abstract regular polyhedron covers a "vertex-faithful" polyhedron with the same number of vertices. We then…
We consider static and spherically symmetric wormhole solutions in extended metric-affine theories of gravity supposing that stability and traversability of these objects can be achieved by means of the geometric degrees of freedom. In…
A bar-joint framework $(G,p)$ in Euclidean $d$-space is rigid if the only edge-length-preserving continuous motions arise from isometries of $\mathbb{R}^d$. In the generic case, rigidity is determined by the generic $d$-dimensional rigidity…
The problem of splitting effects by vertex angles is discussed for nonintegrable rational polygonal billiards. A statistical analysis of the decay dynamics in weakly open polygons is given through the orbit survival probability. Two…
We mostly determine which closed smooth oriented 4-manifolds fibering over lower dimensional manifolds are virtually symplectic, i.e. finitely covered by symplectic 4-manifolds.
The twist polynomial of a delta-matroid was recently introduced by Yan and Jin, who proved a characterization of binary delta-matroids with twist monomials. In this paper, we extend this result to all delta-matroids by proving that any…
The natural matroid of an integer polymatroid was introduced to show that a simple construction of integer polymatroids from matroids yields all integer polymatroids. As we illustrate, the natural matroid can shed much more light on integer…
We define Chern-Schwartz-MacPherson (CSM) cycles of an arbitrary matroid. These are balanced weighted fans supported on the skeleta of the corresponding Bergman fan. In the case that the matroid arises from a complex hyperplane arrangement…
Graphings serve as limit objects for bounded-degree graphs. We define the ``cycle matroid'' of a graphing as a submodular setfunction, with values in [0,1], which generalizes (up to normalization) the cycle matroid of finite graphs. We…
We investigate a family of four-dimensional quantum field theories with weakly interacting ultraviolet fixed points up to four loop order in perturbation theory. Key new ingredients are the three loop gauge contributions to quartic scalar…
The Dirac belt trick is often employed in physics classrooms to show that a $2\pi$ rotation is not topologically equivalent to the absence of rotation whereas a $4\pi$ rotation is, mirroring a key property of quaternions and their…
Motivated by Kontsevich's graph complexes, this paper gives a systematic study of matroid complexes. We construct deletion and contraction bicomplexes on the vector space spanned by matroid classes equipped with ground-set orientations,…
A binary frame template is a device for creating binary matroids from graphic or cographic matroids. Such matroids are said to conform or coconform to the template. We introduce a preorder on these templates and determine the nontrivial…