Related papers: Symmetries of biplanes

A graph $G$ is said to be $d$-distinguishable if there is a labeling of the vertices with $d$ labels so that only the trivial automorphism preserves the labels. The smallest such $d$ is the distinguishing number, Dist($G$). A subset of…

We characterise smooth curves in a smooth cubic threefold whose blow-ups produce a weak-Fano threefold. These are curves $C$ of genus $g$ and degree $d$, such that (i) $2(d-5) \le g$ and $d\le 6$; (ii) $C$ does not admit a 3-secant line in…

We study the automorphisms of a function field of genus $g\geq 2$ over an algebraically closed field of characteristic $p>0$. More precisely, we show that the order of a nilpotent subgroup $G$ of its automorphism group is bounded by $16…

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…

We consider a bipartite distance-regular graph $G$ with diameter $D$ at least 4 and valency $k$ at least 3. We obtain upper and lower bounds for the local eigenvalues of $G$ in terms of the intersection numbers of $G$ and the eigenvalues of…

Let $G$ be a $(2,m,n)$-group and let $x$ be the number of distinct primes dividing $\chi$, the Euler characteristic of $G$. We prove, first, that, apart from a finite number of known exceptions, a non-abelian simple composition factor $T$…

In this paper, we find a two-parameter family of coupled Painlev\'e systems in dimension four with affine Weyl group symmetry of type $D_3^{(2)}$. We also find a four-parameter family of 2-coupled $D_3^{(2)}$-systems in dimension eight with…

A graph $G=(V,E)$ is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. In this paper, we study bipartite $1$-planar graphs with prescribed numbers of vertices in partite sets. Bipartite…

A regular bipartite graph $\Gamma$ is called semisymmetric if its full automorphism group $\mathrm{Aut}(\Gamma)$ acts transitively on the edge set but not on the vertex set. For a subgroup $G$ of $\mathrm{Aut}(\Gamma)$ that stabilizes the…

Let $\mathcal{X}$ be an irreducible, non-singular, algebraic curve defined over a field of odd characteristic $p$. Let $g$ and $\gamma$ be the genus and $p$-rank of $\mathcal{X}$, respectively. The influence of $g$ and $\gamma$ on the…

We investigate the possible structures imposed on a finite group by its possession of an automorphism sending a large fraction of the group elements to their cubes, the philosophy being that this should force the group to be, in some sense,…

Let (N,K) be a nilpotent Gelfand pair, i.e., N is a nilpotent Lie group, K a compact group of automorphisms of N, and the algebra D(N)^K of left-invariant and K-invariant differential operators on N is commutative. In these hypotheses, N is…

In this paper, we study non-hyperelliptic curves of genus $3$ with cyclic automorphism group of order $6$. Over an algebraically closed field $K$ of characteristic $\neq 2,3$, such curves are written as plane quartics $C_r: x^3 z + y^4 + r…

In this article, we study symmetric $(v, k, \lambda)$ designs admitting a flag-transitive and point-primitive automorphism group $G$ whose socle is $PSU_{4}(q)$. We prove that there exist eight non-isomorphic such designs for which…

In this article, we study orientably-regular maps of Euler characteristic $-2p^2$ and classify those that admit a group of orientation-preserving automorphisms of order $10p^2$, where $p$ is a prime number. Along the way, we classify all…

Group theory indicates the existence of a $SO(8) X SO(7) \subset SO(16)$ invariant self-duality equation for a 3-form in 16 dimensions. It is a signal for interesting topological field theories, especially on 8-dimensional manifolds with…

A topological hyperplane is a subspace of R^n (or a homeomorph of it) that is topologically equivalent to an ordinary straight hyperplane. An arrangement of topological hyperplanes in R^n is a finite set H such that k topological…

A classical result of Conway and Pless is that a natural projection of the fixed code of an automorphism of odd prime order of a self-dual binary linear code is self-dual. In this paper we prove that the same holds for involutions under…

We consider symmetric Gelfand pairs $(G,K)$ where $G$ is a compact Lie group and $K$ a subgroup of fixed point of an involutive automorphism. We study the regularity of $K$-bi-invariant matrix coefficients of $G$. The results rely on the…

We characterize the group $\operatorname{Aut}(\mathbb G_2)$ for the symmetrized bidisc $\mathbb G_2:=\{(\lambda_1+\lambda_2,\lambda_1\lambda_2):|\lambda_1|,|\lambda_2|<1\}\sub set\mathbb C^2$.