Related papers: Locally 2-homogeneous block designs

The classification of homogeneous scalar weighted shifts is known. Recently, Kor\'{a}nyi obtained a large class of inequivalent irreducible homogeneous bi-lateral $2$-by-$2$ block shifts. In this paper, we construct two distinct classes of…

We will discuss in this paper homogeneous locally conformally Keahler (or shortly homogeneous l.c.K.) manifolds and locally homogeneous l.c.K. manifolds from various aspects of study in the field of l.c.K. geometry. We will provide a survey…

We classify the pairwise transitive 2-designs, that is, 2-designs such that a group of automorphisms is transitive on the following five sets of ordered pairs: point-pairs, incident point-block pairs, non-incident point-block pairs,…

A locally primitive 2-design is a 2-design admitting an automorphism group $G$ with primitive local actions. It is proved that $G$ is point-primitive, and either $G$ is an almost simple group, or $G$ acting on the points is an affine group.

We extend the 2-representation theory of finitary 2-categories to certain 2-categories with infinitely many objects, denoted locally finitary 2-categories, and extend the classical classification results of simple transitive…

This paper investigates block-transitive automorphism groups of t-(k^2,k,\lambda) designs. Let D be a non-trivial t-(k^2,k,\lambda) design, G \leq \Aut(D) be block-transitive with X\unlhd G\leq \Aut(X), where X = PSL(2,q)(q\geq4). Then q =…

A $3$-$(v,\{4,6\},1)$ design is a configuration of $v$ points and a collection of $4$- and $6$-element subsets called blocks, that jointly contain every 3-element subset exactly once. Using an exhaustive computer search on $v\leq 28$ points…

In the authors's previous work on symmetric differentials and their connection to the topological properties of the ambient manifold, a class of symmetric differentials was introduced: closed symmetric differentials ([BoDeO11] and…

We classify the homogeneous finite-dimensional permutation structures, i.e., homogeneous structures in a language of finitely many linear orders, giving a nearly complete answer to a question of Cameron, and confirming the classification…

A complete classification of locally spherically symmetric four-dimensional Lorentzian spacetimes is given in terms of their local conformal symmetries. The general solution is given in terms of canonical metric types and the associated…

We give a summary of recent results on the explicit local form of the second-order symmetric Lorentzian manifolds in arbitrary dimension, and its global version. These spacetimes turn out to be essentially a specific subclass of plane…

A crossed module constitutes a strict $2$-groupoid $\mathcal{G}$ and a $\mathcal{G}$-valued cocycle on a manifold defines a $2$-bundle. A $2$-connection on this $2$-bundle is given by a Lie algebra $\mathfrak g$ valued $1$-form $A $ and a…

In this paper we introduce a switching for 2-designs. We illustrate this method by applying it to some symmetric (64,28,12) designs. In that way we obtain six new symmetric (64,28,12) designs. Further, we show that this type of switching…

All hypersurface homogeneous locally rotationally symmetric spacetimes which admit conformal symmetries are determined and the symmetry vectors are given explicitly. It is shown that these spacetimes must be considered in two sets. One set…

We classify the finite connected-homogeneous digraphs, as well as the infinite such digraphs with precisely one end. This completes the classification of all the locally finite connected-homogeneous digraphs.

We study locally truncated geometries that are parapolar spaces locally of type A_{n-1,j}(K) with n>6 and j=3,4. Residually connected sheaves over these geometries are constructed. It is proved that these geometries are residually connected…

The present paper is devoted to study 2-local derivations on the Block-type Lie algebra which is an infinite-dimensional Lie algebra with some outer derivations. We prove that every 2-local derivation on the Block-type Lie algebra is a…

We present a classification of the so-called "additive symmetric 2-cocycles" of arbitrary degree and dimension over Z/p, along with a partial result and some conjectures for m-cocycles over Z/p, m > 2. This expands greatly on a result…

Block-transitive Steiner $t$-designs form a central part of the study of highly symmetric combinatorial configurations at the interface of several disciplines, including group theory, geometry, combinatorics, coding and information theory,…

The linked systems of symmetric group divisible designs of type II is introduced, and several examples are obtained from affine resolvable designs and mutually UFS Latin squares. Furthermore, an equivalence between such symmetric group…