Related papers: Cayley Automatic Groups and Numerical Characterist…
A graph $\Ga=(V,E)$ is called a Cayley graph of some group $T$ if the automorphism group $\Aut(\Ga)$ contains a subgroup $T$ which acts on regularly on $V$. If the subgroup $T$ is normal in $\Aut(\Ga)$ then $\Ga$ is called a normal Cayley…
A study of triangulations of cycles in the Cayley diagrams of finitely generated groups leads to a new geometric characterization of hyperbolic groups.
This paper looks at the class of groups admitting normal forms for which the right multiplication by a group element is computed in linear time on a multi-tape Turing machine. We show that the groups $\mathbb{Z}_2 \wr \mathbb{Z}^2$,…
We have developed a theoretical analysis to systematically study the late-time evolution of the Rayleigh-Taylor instability in a finite-sized spatial domain. The nonlinear dynamics of fluids with similar and contrasting densities are…
Non-unique factorizations theory, which started in algebraic number theory, over the years has expanded into several areas of mathematics. Here, we propose yet another branching. We show that some concepts of factorizations theory, such as…
A graph is called an integral graph when all eigenvalues of its adjacency matrix are integers. We study which Cayley graphs over a nonabelian group $$ T_{8n}=\left\langle a,b\mid a^{2n}=b^8=e,a^n=b^4,b^{-1}ab=a^{-1} \right \rangle $$ are…
In this paper we study random induced subgraphs of Cayley graphs of the symmetric group induced by an arbitrary minimal generating set of transpositions. A random induced subgraph of this Cayley graph is obtained by selecting permutations…
Cayley graphs are graphs on algebraic structures, typically groups or group-like structures. In this paper, we have obtained a few results on Cayley graphs on Cyclic groups, powers of cycles, Cayley graphs on some non-abelian groups, and…
In this article we give the basic concept of the "Topological Numbers" in theory of quasiperiodic functions. The main attention is paid to apperance of such values in transport phenomena including Galvanomagnetic phenomena in normal metals…
Let $\Gamma$ be a group and $(\Gamma_n)_{n=1} ^{\infty}$ be a descending sequence of finite-index normal subgroups. We establish explicit upper bounds on the diameters of the directed Cayley graphs of the $\Gamma/\Gamma_n$ , under some…
Products of shifted characteristic polynomials, and ratios of such products, averaged over the classical compact groups are of great interest to number theorists as they model similar averages of L-functions in families with the same…
In spite of the plethora of success stories with graph neural networks (GNNs) on modelling graph-structured data, they are notoriously vulnerable to over-squashing, whereby tasks necessitate the mixing of information between distance pairs…
In the past few decades, quantum algorithms have become a popular research area of both mathematicians and engineers. Among them, uniform mixing provides a uniform probability distribution of quantum information over time which attracts a…
The unitary Cayley graph of $\mathbb{Z}/n\mathbb{Z}$, denoted $X_n$, is the graph on $\{0,\dots,n-1\}$ where vertices $a$ and $b$ are adjacent if and only if $\gcd(a-b,n) = 1$. We answer a question of Defant and Iyer by constructing a…
We study first passage percolation (FPP) with stationary edge weights on Cayley graphs of finitely generated virtually nilpotent groups. Previous works of Benjamini-Tessera and Cantrell-Furman show that scaling limits of such FPP are given…
The degree-diameter problem seeks to find the largest possible number of vertices in a graph having given diameter and given maximum degree. Very often the problem is studied for restricted families of graph such as vertex-transitive or…
We construct a new family of Cayley automatic representations of semidirect products $\mathbb{Z}^n \rtimes_A \mathbb{Z}$ for which none of the projections of the normal subgroup $\mathbb{Z}^n$ onto each of its cyclic components is finite…
We introduce invariants, called shifting numbers, that measure the asymptotic amount by which an autoequivalence of a triangulated category translates inside the category. The invariants are analogous to Poincare translation numbers that…
In this note we revisit the problem of explicitly computing tree-level scattering amplitudes in various theories in any dimension from worldsheet formulas. The latter are known to produce cubic-tree expansion of tree amplitudes with…
We show that every finitely generated group G with an element of order at least $(5rank(G))^{12}$ admits a locally finite directed Cayley graph with automorphism group equal to G. If moreover G is not generalized dihedral, then the above…