Related papers: Combinatorial geometry takes the lead
We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed…
Within this research, two combinatorial bijections using Young diagrams were studied. The first is a special case of a bijective correspondence between two classes of combinatorial objects. Its proof, based on Young diagrams, establishes…
The modern theory of homogeneous structures begins with the work of Roland Fra\"iss\'e. The theory developed in the last seventy years is placed in the border area between combinatorics, model theory, algebra, and analysis. We turn our…
Linear superposition of gravitational fields is shown to be possible for a large class of spacetimes, in some specific coordinates. Explicit examples are presented.
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
We study the moduli space of euclidean structures with cone points on a surface, and describe a decomposition into cells each of which corresponds to a given combinatorial type of Delaunay tessellation. We use some of the ideas to study…
The study of combinatorial properties of mathematical objects is a very important research field and continued fractions have been deeply studied in this sense. However, multidimensional continued fractions, which are a generalization…
An $r$-segment hypergraph $H$ is a hypergraph whose edges consist of $r$ consecutive integer points on line segments in $\mathbb{R}^2$. In this paper, we bound the chromatic number $\chi(H)$ and covering number $\tau(H)$ of hypergraphs in…
We describe an algebra G of diagrams which faithfully gives a diagrammatic representation of the structures of both the Heisenberg-Weyl algebra H - the associative algebra of the creation and annihilation operators of quantum mechanics -…
This is the seventh article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. It discusses an interesting class of observables localised on surfaces that attracts steadily growing attention.…
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…
The purpose of this paper is twofold: 1. we prove the triangulability of smooth orbifolds with corners, generalizing the same statement for orbifolds. 2. based on 1, we propose a new homology theory. We call it geometric homology theory…
Before retiring, looking back to forty years of writing and publishing scientific papers, I decided to present to the scientific community a selection of my scientific works. I chose mostly articles published in prestigious journals or…
In this paper, we provide a unified definition of mediated graph, a combinatorial structure with multiple applications in mathematical optimization. We study some geometric and algebraic properties of this family of graphs and analyze…
These are lecture notes mainly aimed at graduate students on selected aspects of generalized geometry: in particular generalized complex and Kaehler structures and generalized holomorphic bundles. They are based on lectures given in March…
Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric…
We explore connections between the generalized multiplicities of square-free monomial ideals and the combinatorial structure of the underlying hypergraphs using methods of commutative algebra and polyhedral geometry. For instance, we show…
I review some aspects of supersymmetric grand unification and emphasize a recent development in the area of gauge coupling unification.
In this article we introduce a class of generalisations of the Jordan-Schwinger (JS) map which realises the recent proposed generalised sl(2) (G-sl(2)) algebra via two independent Generalised Heisenberg Algebras (GHA). Although the GHA and…
The GUT-based approach to physics has been attractive since it was first put forward close to thirty years ago; it has been enriched by new ideas, notably supersymmetry and strings; and there are real hints that it is on the right track,…