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Now showing items 1-10 of 11

#### Most primitive groups are full automorphism groups of edge-transitive hypergraphs

(2015-01-01) - Journal article,

We prove that, for a primitive permutation group G acting on a set of size n, other than the alternating group, the probability that Aut(X,YG) = G for a random subset Y of X, tends to 1 as n tends to infinity. So the ...

#### Constructing flag-transitive, point-imprimitive designs

(2016-05-04) - Journal article,

We give a construction of a family of designs with a specified point-partition and determine the subgroup of automorphisms leaving invariant the point-partition. We give necessary and sufficient conditions for a design in ...

#### Most switching classes with primitive automorphism groups contain graphs with trivial groups

(2015-06) - Journal article,

The operation of switching a graph Gamma with respect to a subset X of the vertex set interchanges edges and non-edges between X and its complement, leaving the rest of the graph unchanged. This is an equivalence relation ...

#### Guessing games on triangle-free graphs

(2016) - Journal article,

The guessing game introduced by Riis is a variant of the "guessing your own hats" game and can be played on any simple directed graph G on n vertices. For each digraph G, it is proved that there exists a unique guessing ...

#### The classification of partition homogeneous groups with applications to semigroup theory

(2016-04-15) - Journal article,

Let λ=(λ1,λ2,...) be a partition of n, a sequence of positive integers in non-increasing order with sum n. Let Ω:={1,...,n}. An ordered partition P=(A1,A2,...) of Ω has type λ if |Ai|=λi.Following Martin and Sagan, we say ...

#### String C-groups as transitive subgroups of Sn

(2016-02-01) - Journal article,

If Γ is a string C-group which is isomorphic to a transitive subgroup of the symmetric group Sn (other than Sn and the alternating group An), then the rank of Γ is at most n/2+1, with finitely many exceptions (which are ...

#### Computing in permutation groups without memory

(2014-11-02) - Journal article,

Memoryless computation is a new technique to compute any function of a set of registers by updating one register at a time while using no memory. Its aim is to emulate how computations are performed in modern cores, since ...

#### Computing in matrix groups without memory

(2014-11-02) - Journal article,

Memoryless computation is a novel means of computing any function of a set of registers by updating one register at a time while using no memory. We aim to emulate how computations are performed on modern cores, since they ...

#### Sesqui-arrays, a generalisation of triple arrays

(2018-06-01) - Journal article,

A triple array is a rectangular array containing letters, each letter occurring equally often with no repeats in rows or columns, such that the number of letters common to two rows, two columns, or a row and a column are ...

#### On optimality and construction of circular repeated-measurements designs

(2017-01) - Journal article,

The aim of this paper is to characterize and construct universally optimal designs among the class of circular repeated-measurements designs when the parameters do not permit balance for carry-over effects. It is shown ...