We show that the countable universal-homogeneous partial order (P,<) has a generic automorphism as defined by the second author, namely that it lies in a comeagre conjugacy class of Aut(P,<). For this purpose, we work with ‘determined’ partial finite automorphisms that need not be automorphisms of finite substructures (as in the proofs of similar results for other countable homogeneous structur...

1. Abstract A classiication was given in 1, 12, 13] of all the countable k-CS-transitive cycle-free partial orders for k 3. Here the elementary theories of these structures and their automorphism groups are examined, and it is shown that in many cases we can distinguish the structures or their groups by means of their rst or second order properties. The small index property is established for w...

In this paper, we first prove some general results on the number of fixed points of collineations of finite partial geometries, and on the number of absolute points of dualities of partial geometries. In the second part of the paper, we establish the number of isomorphism classes of partial geometries arising from a Thas maximal arc constructed from a (finite) Suzuki-Tits ovoid in a classical p...

A partial linear space is a non-empty set of points, provided with a collection of subsets called lines such that any pair of points is contained in at most one line and every line contains at least two points. Graphs and linear spaces are particular cases of partial linear spaces. A partial linear space which is neither a graph nor a linear space is called proper. The aim of this paper is to c...

Abstract: The left-right models provide an explanation for the parity asymmetry in the the Standard Model (SM). To further understand the origin of the left-right symmetry, we study a partial unification model based on SU(4)W×U(1)B−L which can be broken down to the minimal left-right model either through the Higgs mechanism in four dimensions or through the five-dimensional orbifold gauge symme...

Motivated by questions in the study of relative trace formulae, we construct a generalization Grothendieck's simultaneous resolution over regular locus certain symmetric pairs. We use this space to prove version results Donagi and Gaitsgory about automorphism sheaf stabilizers. also obtain partial toward applications Springer theory for spaces.

We establish natural bijections between three different classes of combinatorial objects; namely certain families of locally 2–arc transitive graphs, partial linear spaces, and homogeneous factorisations of arc-transitive graphs. Moreover, the bijections intertwine the actions of the relevant automorphism groups. Thus constructions in any of these areas provide examples for the others.

We examine the designs produced by different types of difference families. Difference families have long been known to produce designs with well behaved automorphism groups. These designs provide the elegant solutions desired for applications. In this work, we explore the following question: Does every (named) design have a difference family analogue? We answer this question in the affirmative ...