Related papers: Classification of Six-Point Metrics

In this paper, we propose a topological classification of points for 2D discrete binary images. This classification is based on the values of the calculus of topological numbers. Six classes of points are proposed: isolated point, interior…

We show that for fixed $d>3$ and $n$ growing to infinity there are at least $(n!)^{d-2 \pm o(1)}$ different labeled combinatorial types of $d$-polytopes with $n$ vertices. This is about the square of the previous best lower bounds. As an…

In this note we study line and conic arrangements associated to sextactic and type 9 points on the Fermat cubic $F$ and we provide explicit coordinates for each of the 72 type 9 points on $F$.

This paper is a sequel to the paper \cite{refGH}. We relate the matroid notion of a combinatorial geometry to a generalization which we call a configuration type. Configuration types arise when one classifies the Hilbert functions and…

In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be…

Observations suggest that our universe is spatially flat on the largest observable scales. Exactly six different compact orientable three-dimensional manifolds admit flat metrics. These six manifolds are therefore the most natural choices…

In this note we find the metrics of 6-dimensional h-spaces of the [3(21)], [(32)1], [(321)] types and then determine the quadratic first integrals of the geodesic equations of these h-spaces.

In this paper, we introduce a new category of mappings within metric spaces, specifically focusing on three-point analogs of the well-established Chatterjea type mappings. We demonstrate that Chatterjea type mappings and their three-point…

We present the complete set of universal one-loop beta functions of cubic gravity in six dimensions. The system admits over 8000 distinct fixed points, of which more than 200 are real. Some of them might be relevant for the quantisation of…

We extend a classification of irreducible, almost-commutative geometries whose spectral action is dynamically non-degenerate, to internal algebras that have six simple summands. We find essentially four particle models: An extension of the…

We construct examples of nonresolvable generalized $n$-manifolds, $n\geq 6$, with arbitrary resolution obstruction, homotopy equivalent to any simply connected, closed $n$-manifold. We further investigate the structure of generalized…

We give coordinate-minimal geometric realizations in general position of all 865 vertex-minimal triangulations of the orientable surface of genus 2 in the 4x4x4-cube.

A census is presented of all closed non-orientable 3-manifold triangulations formed from at most seven tetrahedra satisfying the additional constraints of minimality and P^2-irreducibility. The eight different 3-manifolds represented by…

A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…

In this paper, we study $6$-dimensional GKM manifolds with $4$ fixed points. We classify all possible GKM graphs, and for each type of graph we construct a manifold, proving the existence. We show that six types occur. (P1) complex…

The article contains some important classes of multisets. Combinatorial proofs of problems on the number of m-submultisets and m-permutations of multiset elements are considered and effective algorithms for their calculation are given. In…

We study flips in hypertriangulations of planar points sets. Here a level-$k$ hypertriangulation of $n$ points in the planes is a subdivision induced by the projection of a $k$-hypersimplex, which is the convex hull of the barycenters of…

In this note we present three representations of a 248-dimensional Lie algebra, namely the algebra of Lie point symmetries admitted by a system of five trivial ordinary differential equations each of order forty-four, that admitted by a…

We construct 2^{\Omega(n^{5/4})} combinatorial types of triangulated 3-spheres on n vertices. Since by a result of Goodman and Pollack (1986) there are no more than 2^{O(n log n)} combinatorial types of simplicial 4-polytopes, this proves…

We formulate a conjecture relating the topology of a manifold's universal cover with the existence of metrics with positive $m$-intermediate curvature. We prove the result for manifolds of dimension $n\in\{3,4,5\}$ and for most choices of…