Related papers: Group divisible designs with block size five: dire…

For a group G and positive interger m, Gm denotes the subgroup generated by the elements gm where g runs through G. The subgroups not of the form Gm are called nonpower subgroups. We extend the classification of groups with few nonpower…

In this paper we introduce a construction of directed strongly regular graphs from smaller ones using equitable partitions. Each equitable partition of a single DSRG satisfying several conditions leads to an infinite family of directed…

Let $\mathcal{D}$ be a nontrivial $3$-$(v,k,1)$ design admitting a block-transitive group $G$ of automorphisms. A recent work of Gan and the second author asserts that $G$ is either affine or almost simple. In this paper, it is proved that…

The design spectrum of a simple graph $G$ is the set of positive integers $n$ such that there exists an edgewise decomposition of the complete graph $K_n$ into $n(n - 1)/(2 |E(G)|)$ copies of $G$. We compute the design spectra for 7788…

A \textbf{single change covering design} is a $v$-set $X$ and an ordered list $\cL$ of $b$ blocks of size $k$ where every $t$-set must occur in at least one block. Each pair of consecutive blocks differs by exactly one element. A single…

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…

The action dimension of a discrete group $G$ is the minimum dimension of contractible manifold that admits a proper $G$-action. We compute the action dimension of the direct limit of a simple complex of groups for several classes of…

In this paper, we give a new method for constructing LCD codes. We employ group rings and a well known map that sends group ring elements to a subring of the $n \times n$ matrices to obtain LCD codes. Our construction method guarantees that…

The resolutions and maximal sets of compatible resolutions of all 2-(120,8,1) designs arising frommaximal (120,8)-arcs in the known projective planes of order 16 are computed. It is shown that each of these designs is embeddable in a unique…

Balanced incomplete block designs (BIBDs) are a class of designs with v treatments and b blocks of size k that are optimal with regards to a wide range of optimality criteria, but it is not clear which designs to choose for combinations of…

We give sufficient conditions for a linear differential equation to have a given semisimple group as its Galois group. For any linear algebraic group G given as a semidirect product of a finite subgroup and a normal subgroup that is a…

We show that a certain triangulation of CAT(0) triangle-pentagon complexes is $7$-located and locally $5$-large. Hereby we give examples of $7$-located, locally $5$-large groups.

Motivated by a question by D. Mumford : can a computer classify all surfaces with $p_g = 0$ ? we try to show the complexity of the problem. We restrict it to the classification of the minimal surfaces of general type with $p_g = 0, K^2 = 8$…

Optimal block designs in small blocks are explored when the treatments have a natural ordering and interest lies in comparing consecutive pairs of treatments. We first develop an approximate theory which leads to a convenient multiplicative…

So far, it has been proven that if $G$ is an abelian group , then the diameter of $G^n$ with respect to any generating set is $O(n)$; and if $G$ is nilpotent, symmetric or dihedral, then there exists a generating set of minimum size, for…

We try to embed a t-design in a finite commutative group in such a way that the sum of the k points of a block is zero. We can compute the number of blocks of the boolean 2-design having all the non zero vectors of $(Z_2)^n$ as the set of…

In this paper, we present a new method to construct solvable groups with derived length four and four character degrees. We then use this method to present a number of new families of groups with derived length four and four character…

In this paper we provide a generalization of the MPS construction of blocking sets of $PG(r,q^n)$ using subspaces of dimension $s\leq n-2$. By this construction, we determine a new non-planar example in $PG(3,q^6)$.

To a family of smooth projective cubic surfaces one can canonically associate a family of abelian fivefolds. In characteristic zero, we calculate the Hodge groups of the abelian varieties which arise in this way. In arbitrary characteristic…

In this article we describe the general and special projectivity groups for all irreducible residues of all thick, irreducible, spherical buildings of type $ \mathsf{B_{n}}$, $ \mathsf{C_{n}}$ and $\mathsf{F_4}$, and rank at least 3. This…