Related papers: A new structure for difference matrices over abeli…

The concept of matchings originated in group theory to address a linear algebra problem related to canonical forms for symmetric tensors. In an abelian group $(G,+)$, a matching is a bijection $f: A \to B$ between two finite subsets $A$ and…

Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…

We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular…

The circular external difference family and its strong version, which themselves are of independent combinatorial interest, were proposed as variants of the difference family to construct new unconditionally secure non-malleable threshold…

Davis and Jedwab (1997) established a great construction theory unifying many previously known constructions of difference sets, relative difference sets and divisible difference sets. They introduced the concept of building blocks, which…

Block designs are combinatorial structures in which each pair of a set of varieties appears together in a fixed number of blocks. Complete graphs are graphs in which every pair of vertices are adjacent. We present some new constructions of…

Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation, while building…

We study dp-minimal infinite profinite groups that are equipped with a uniformly definable fundamental system of open subgroups. We show that these groups have an open subgroup $A$ such that either $A$ is a direct product of countably many…

Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…

Difference sets and their generalisations to difference families arise from the study of designs and many other applications. Here we give a brief survey of some of these applications, noting in particular the diverse definitions of…

The fundamental group of the complement of a hyperplane arrangement plays an important role in studying the corresponding arrangements. In particular, for large families of hyperplane arrangements, this fundamental group, being isomorphic…

Identifying and explaining the structure of complex networks at different scales has become an important problem across disciplines. At the mesoscale, modular architecture has attracted most of the attention. At the macroscale, other…

A theory of matchings for finite subsets of an abelian group, introduced in connection with a conjecture of Wakeford on canonical forms for homogeneous polynomials, has since been extended to the setting of field extensions and to that of…

The genus spectrum of a finite group $G$ is the set of all $g$ such that $G$ acts faithfully on a compact Riemann surface of genus $g$. It is an open problem to find a general description of the genus spectrum of the groups in interesting…

We investigate the mutual relations between the centers of different elements in the deconstruction lattice of a 2D conformal model, and show how these can be described using exact sequences of abelian groups. In particular, we exhibit a…

For each odd integer $p > 1$, we construct infinitely many pairwise non-diffeomorphic irreducible smooth structures on a definite 4-manifold with infinite fundamental group whose abelianization is $\Z/2p\Z\times \Z/2\Z$.

The study of geometric group theory has suggested several theorems related to subdivision tilings that have a natural hyperbolic structure. However, few examples exist. We construct subdivision tilings for the complement of every…

Conference matrices are used to define complex structures on real vector spaces. Certain lattices in these spaces become modules for rings of quadratic integers. Multiplication of these lattices by non-principal ideals yields simple…

A triangle presentation is a combinatorial datum that encodes the action of a group on a $2$-dimensional triangle complex with prescribed links, which is simply transitive on the vertices. We provide the first infinite family of triangle…

For an oriented surface link $S$, we can take a satellite construction called a 2-dimensional braid over $S$, which is a surface link in the form of a covering over $S$. We demonstrate that 2-dimensional braids over surface links are useful…