Related papers: Thinness of some hypergeometric groups in Sp(6)

A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre $\beta$ ensemble, characterised by the Dyson parameter $\beta$, and the Laguerre…

The automorphism group $\Sigma$ of a compact topological projective plane with a $16$-dimensional point space is a locally compact group. If the dimension of $\Sigma$ is at least $29$, then $\Sigma$ is known to be a Lie group. For the…

The exceptional Dehn filling conjecture of the second author concerning the relationship between exceptional slopes $\alpha, \beta$ on the boundary of a hyperbolic knot manifold $M$ has been verified in all cases other than small Seifert…

We construct families of hyperbolic hypersurfaces of degree $2n$ in the projective space $\mathbb{P}^n(\mathbb{C})$ for $3 \leq n \leq 6$.

The rank of an $A$-hypergeometric $D$-module $M_A(\beta)$, associated with a full rank $(d\times n)$-matrix $A$ and a vector of parameters $\beta\in \mathbb{C}^d$, is known to be the normalized volume of $A$, denoted $\mathrm{vol}(A)$, when…

We derive an expression for the entropy of a dark matter halo described by a Navarro-Frenk-White model with a core. The comparison of this entropy with the one of dark matter at the freeze-out era allows us to constraint the parameter space…

An algebraic structure is said to be congruence permutable if its arbitrary congruences $\alpha$ and $\beta$ satisfy the equation $\alpha \circ \beta =\beta \circ \alpha$, where $\circ$ denotes the usual composition of binary relations. For…

Compact polyhedra of cubic point symmetry Oh, exhibit surfaces of planar sections (facets) characterized by normal vector families {abc} with up to 48 members each, compatible with Oh symmetry. We focus first on polyhedra confined by facets…

Let $F$ be a group whose abelianization is $\Z^k$, $k\geq 2.$ An element of $F$ is called visible if its image in the abelianization is visible, that is, the greatest common divisor of its coordinates is 1. In this paper we compute three…

We investigate inverse thickness $1/\Delta$ and the integral Menger curvature energies $\mathcal{U}_{p}^{\alpha}$, $\mathcal{I}_{p}^{\alpha}$ and $\mathcal{M}_{p}^{\alpha}$, to find that finite $1/\Delta$ or $\mathcal{U}_{p}^{\alpha}$…

We derive explicit isomorphisms between certain congruence subgroups of the Siegel modular group, the Hermitian modular group over an arbitrary imaginary-quadratic number field and the modular group over the Hurwitz quaternions of degree 2…

We introduce a parameter space containing all algebraic integers $\beta\in(1,2]$ that are not Pisot or Salem numbers, and a sequence of increasing piecewise continuous function on this parameter space which gives a lower bound for the…

Let $M$ be a simple 3-manifold, and $F$ be a component of $\partial M$ of genus at least 2. Let $\alpha$ and $\beta$ be separating slopes on $F$. Let $M(\alpha)$ (resp. $M(\beta)$) be the manifold obtained by adding a 2-handle along…

It is proved that if $G$ is a $t$-tough graph of order $n$ and minimum degree $\delta$ with $t>1$ then either $G$ has a cycle of length at least $\min\{n,2\delta+5\}$ or $G$ is the Petersen graph.

We show that in the random hyperbolic graph model as formalized by Gugelmann et al. in the most interesting range of $\frac12 < \alpha < 1$ the size of the second largest component is $\Theta((\log n)^{1/(1-\alpha)})$, thus answering a…

In this paper, we determine the reduced automorphism groups of hyperelliptic curves of a small genus in characteristic $2$, when they are of $2$-rank $0$. Such a curve is an Artin-Schreier curve defined in the form $y^2-y=f(x)$ for a…

We show that every word hyperbolic, surface-by-(noncyclic) free group Gamma is as rigid as possible: the quasi-isometry group of Gamma equals the abstract commensurator group Comm(Gamma), which in turn contains Gamma as a finite index…

Let Gamma < SL(2,Z) be a free, finitely generated Fuchsian group of the second kind with no parabolics, and fix two primitive non-zero vectors v0, w0 in Z^2. We consider the set S of all integers occurring in <v0 gamma,w0>, for gamma in…

We compute the exact and limiting smallest eigenvalue distributions for two classes of $\beta$-Jacobi ensembles not covered by previous studies. In the general $\beta$ case, these distributions are given by multivariate hypergeometric…

Let $f(z)={}_nF_{n-1}(\mathbf{\alpha},\mathbf{\beta})$ be the hypergeometric series with parameters $\mathbf{\alpha} = (\alpha_1,\ldots,\alpha_n)$ and $\mathbf{\beta} = (\beta_1,\ldots,\beta_{n-1},1)$ in $(\mathbb{Q}\cap(0,1])^n$, let…