Related papers: $\mathrm{ EA}(q)$-additive Steiner 2-designs

Graphical designs are subsets of vertices of a graph that perfectly average a selected set of eigenvectors of the Graph Laplacian. We show that in highly-structured graphs, graphical designs can coincide with highly structured and…

In this paper, we present some criteria for the $2$-$q$-log-convexity and $3$-$q$-log-convexity of combinatorial sequences, which can be regarded as the first column of certain infinite triangular array $[A_{n,k}(q)]_{n,k\geq0}$ of…

This paper gives a construction of group divisible designs on the binary extension fields with block sizes 3, 4, 5, 6, and 7, respectively, which is motivated from the decoding of binary quadratic residue codes. A conjecture is proposed for…

The dimension of a block design is the maximum positive integer $d$ such that any $d$ of its points are contained in a proper subdesign. Pairwise balanced designs PBD$(v,K)$ have dimension at least two as long as not all points are on the…

A combinatorial block design $D$ is called $3$-pyramidal if there exists a subgroup $G$ of $\mbox{Aut}(D)$ fixing $3$ points and acting regularly on the other points. If this happens, we say that the design is $3$-pyramidal under $G$. In…

A Ryser design $\mathcal{D}$ on $v$ points is a collection of $v$ proper subsets (called blocks) of a point-set with $v$ points satisfying (i) every two blocks intersect each other in $\lambda$ points for a fixed $\lambda < v$ (ii) there…

The parameters 2-(36,15,6) are the smallest parameters of symmetric designs for which a complete classification up to isomorphism is yet unknown. Bouyukliev, Fack and Winne classified all 2-$(36,15,6)$ designs that admit an automorphism of…

In this article we study the endomorphism algebras of abelian varieties $A$ defined over a given number field $K$ with large cyclic 2-torsion fields. A key step in doing so is to provide criteria for all the endomorphisms of $A$ to be…

We provide new computations in bounded cohomology: A group is boundedly acyclic if its bounded cohomology with trivial real coefficients is zero in all positive degrees. We show that there exists a continuum of finitely generated…

A Ryser design $\mathcal{D}$ on $v$ points is a collection of $v$ proper subsets (called blocks) of a point-set with $v$ points such that every two blocks intersect each other in $\lambda$ points (and $\lambda < v$ is a fixed number) and…

Stirling numbers of both kinds are linked to each other via two combinatorial identities due to Schl\"afli and Gould. Using q-analogs of Stirling numbers defined as inversion generating functions, we provide q-analogs of the two identities.…

Let $\mathcal{R}_e=GR(p^e,r)[y]/\langle g(y),p^{e-1}y^t\rangle$ be a finite commutative chain ring, where $p$ is a prime number, $GR(p^e,r)$ is the Galois ring of characteristic $p^e$ and rank $r,$ $t$ and $k$ are positive integers…

A 2-covering for a finite group $G$ is a set of proper subgroups of $G$ such that every pair of elements of $G$ is contained in at least one subgroup in the set. The minimal number of subgroups needed to 2-cover a group $G$ is called the…

In this article, we prove that if $\mathcal{D}$ is a $2$-design with $k=7$ admitting flag-transitive almost simple automorphism group with socle an alternating group, then $\mathcal{D}$ is $PG_{2}(3,2)$ with parameter set $(15,7,3)$ and…

It is clear that the full automorphism group of the $(15,8,4)$-design of points and hyperplane complements of ${\rm PG}(3,2)$ is ${\rm GL}(4,2)$. Using methods of point-line geometries, we determine the full automorphism groups of the…

Solvable Lie algebras having at least one Abelian descending central ideal are studied. It is shown that all such Lie algebras can be built up from canonically defined ideals. The nature of such ideals is elucidated and their construction…

For an arbitrary ring $A$, we study the abelianization of the elementary group $\textrm{E}_2(A)$. In particular, we show that for a commutative ring $A$ there exists an exact sequence \[ K_2(2,A)/C(2,A) \to A/M \to…

A $t\text{-}(n,k,\lambda;q)$-design is a set of $k$-subspaces, called blocks, of an $n$-dimensional vector space $V$ over the finite field with $q$ elements such that each $t$-subspace is contained in exactly $\lambda$ blocks. A partition…

The Stirling numbers of type $B$ of the second kind count signed set partitions. In this paper we provide new combinatorial and analytical identities regarding these numbers as well as Broder's $r$-version of these numbers. Among these…

It is shown that a refined version of a q-analogue of the Eulerian numbers together with the action, by conjugation, of the subgroup of the symmetric group $S_n$ generated by the $n$-cycle $(1,2,...,n)$ on the set of permutations of fixed…