Related papers: Higher secondary polytopes and regular plabic grap…
Symmetric edge polytopes are a class of lattice polytopes constructed from finite simple graphs. In the present paper we highlight their connections to the Kuramoto synchronization model in physics -- where they are called adjacency…
Toric topology assigns to each simple convex $n$-polytope $P$ with $m$ facets an $n$-dimensional real moment angle manifold $\mathbb RZ_P$ with a canonical action of $\mathbb Z_2^m=(\mathbb Z/2\mathbb Z)^m$. We consider (non-necessarily…
We give two "lifting" constructions of strongly regular Cayley graphs. In the first construction we "lift" a cyclotomic strongly regular graph by using a subdifference set of the Singer difference set. The second construction uses quadratic…
We develop a spectral approach to Sidorenko-type inequalities and apply it to establish sharp edge-spectral supersaturation results. Let $H$ be a bipartite graph with $v$ vertices and $e$ edges, where $v\le e$, and write $M(G)=2e(G)$. We…
In the Grassmannian formulation of the S-matrix for planar $\mathcal{N}=4$ Super Yang-Mills, $N^{k-2}MHV$ scattering amplitudes for $k$ negative and $n-k$ positive helicity gluons can be expressed, by an application of the global residue…
Gromov asked whether every one-ended word-hyperbolic group contains a hyperbolic surface group. We prove that every one-ended double of a free group has a hyperbolic surface subgroup if (1) the free group has rank two, or (2) every…
In 1983, Conway-Gordon showed that for every spatial complete graph on 6 vertices, the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2, and for every spatial complete graph on 7 vertices,…
The main aim of this paper is to provide a method which allows finding limiting shapes of symbolic generic initial systems of higher-dimensional subvarieties of P^n. M. Mustata and S. Mayes established a connection between volumes of…
We describe a new sequence of polytopes which characterize A_infinity maps from a topological monoid to an A_infinity space. Therefore each of these polytopes is a quotient of the corresponding multiplihedron. Later term(s) in our sequence…
We augment the list of finite universal locally toroidal regular polytopes of type {3,3,4,3,3} due to P.McMullen and E.Schulte, adding as well as removing entries. This disproves a related long-standing conjecture. Our new universal…
We explore the relation between the singleton and adjoint modules of higher-spin algebras via so(2,d) characters. In order to relate the tensor product of the singleton and its dual to the adjoint module, we consider a heuristic formula…
Let $\Sigma$ be a closed subset of $\mathbb{R}^ {n+1}$ which is parabolic Ahlfors-David regular and assume that $\Sigma$ satisfies a 2-sided corkscrew condition. Assume, in addition, that $\Sigma$ is either time-forwards Ahlfors-David…
We investigate which topological spaces can be constructed as topological realisations of higher-rank graphs. We describe equivalence relations on higher-rank graphs for which the quotient is again a higher-rank graph, and show that…
This paper lays out the foundations of graded $K$-theory for Leavitt algebras associated with higher-rank graphs, also known as Kumjian-Pask algebras, establishing it as a potential tool for their classification. For a row-finite $k$-graph…
A concept of generalized regular polytope is introduced in this work. The number of its (1...n-1)-dimensional elements is not necessarily integer, though all the combinatorial and metric properties meet those of regular polytopes in a…
This note provides an introduction to selected topics in algebraic graph theory, including strongly regular graphs, Steiner systems, and automorphism groups. We describe constructions and properties of notable graphs such as the Petersen…
This paper investigates the problem of listing faces of combinatorial polytopes, such as hypercubes, permutahedra, associahedra, and their generalizations. Firstly, we consider the face lattice, which is the inclusion order of all faces of…
We resolve the existence of mixed 't Hooft anomalies between the electric and magnetic (solitonic) symmetries in $\sigma$-models and gauge theories. We identify the anomaly as naturally originating from a higher group in the Whitehead tower…
A proof is given of Polyakov conjecture about the auxiliary parameters of the SU(1,1) Riemann-Hilbert problem for general elliptic singularities. Such a result is related to the uniformization of the the sphere punctured by n conical…
The scissors congruence conjecture for the unimodular group is an analogue of Hilbert's third problem, for the equidecomposability of polytopes. Liu and Osserman studied the Ehrhart quasi-polynomials of polytopes naturally associated to…