Related papers: On circular external difference families
In [12] was introduced, for cyclic groups, the class of partially filled arrays of the non-zero sum Heffter array that are, as the Heffter arrays, related to difference families, graph decompositions, and biembeddings. Here we generalize…
Cyclic codes, as a crucial subclass of linear codes, exhibit broad applications in communication systems, data storage systems, and consumer electronics, primarily attributed to their well-structured algebraic properties. Let $p$ denote an…
Some relations between families of two-character CFTs are explained using a slightly generalised coset construction, and the underlying theories (whose existence was only conjectured based on the modular differential equation) are…
According to \cite{Dvz}, we know that the class of all EMV-algebras, $\mathsf{EMV}$, is not a variety, since it is not closed under the subalgebra operator. The main aim of this work is to find the least variety containing $\mathsf{EMV}$.…
Given a family $\mathcal{F}=\{A_1,\dots,A_s\}$ of subsets of $\mathbb{Z}_n$, define $\Delta \mathcal{F}$ to be the multiset of all (cyclic) distances dist$(x,y)$, where $\{x,y\} \subset A_i$, $x \neq y$, for some $i=1,\dots,s$. Taking…
We establish a parameter-dependent pseudo-differential calculus on an infinite cylinder, regarded as a manifold with conical exits to infinity. The parameters are involved in edge-degenerate form, and we formulate the operators in terms of…
Understanding causal relationships between variables is fundamental across scientific disciplines. Most causal discovery algorithms rely on two key assumptions: (i) all variables are observed, and (ii) the underlying causal graph is…
Let $m$ and $r$ be integers with $m \ge r \ge 3$ and let $G$ be an $r$-regular graph of even order. Let $M$ be a matching in $G$ of size $m$ such that each pair of edges in $M$ is at distance at least $3$. In 2023, Aldred et al. proved that…
We consider cyclic codes $\mathcal{C}_\mathcal{L}$ associated to quadratic trace forms in $m$ variables $Q_R(x) = \operatorname{Tr}_{q^m/q}(xR(x))$ determined by a family $\mathcal{L}$ of $q$-linearized polynomials $R$ over…
Verifying a suspicion of Propp and Reiner concerning the cyclic sieving phenomenon (CSP), M. Thiel introduced a Catalan object called noncrossing $(1,2)$-configurations (denoted by $X_n$), which is a class of set partitions of $[n-1]$. More…
Given a strict partial order $\Delta$ on a set $\Lambda$ and an arbitrary ring $R$ with $1\neq 0$, the corresponding McLain group $M(\Delta)$ has been studied in depth. We construct a larger family of McLain groups $G(\Delta)$, where…
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
Causal effect identification using causal graphs is a fundamental challenge in causal inference. While extensive research has been conducted in this area, most existing methods assume the availability of fully specified directed acyclic…
The purpose of this work is to provide details about the construction of the Chern character for categorical sheaves mentioned in our previous work "Chern character, loop spaces and derived algebraic geometry". For this, we introduce and…
A group classification of first-order delay ordinary differential equation (DODE) accompanied by an equation for delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs) which…
In this article we study the existence of limit cycles in families of piecewise smooth differential equations having the unit circle as discontinuity region. We consider families presenting singularities of center or saddle type, visible or…
An affine semigroup is a finitely generated subsemigroup of $(\mathbb Z_{\ge 0}^d, +)$, and a numerical semigroup is an affine semigroup with $d = 1$. A growing body of recent work examines shifted families of numerical semigroups, that is,…
A subset $B$ of an Abelian group $G$ is called a difference basis of $G$ if each element $g\in G$ can be written as the difference $g=a-b$ of some elements $a,b\in B$. The smallest cardinality $|B|$ of a difference basis $B\subset G$ is…
A dessin is a 2-cell embedding of a connected $2$-coloured bipartite graph into an orientable closed surface. A dessin is regular if its group of orientation- and colour-preserving automorphisms acts regularly on the edges. In this paper we…
For nearly a century, mathematicians have been developing techniques for constructing abelian automorphism groups of combinatorial objects, and, conversely, constructing combinatorial objects from abelian groups. While abelian groups are a…