Related papers: Simultaneous representations of semilattices by la…

To any fixed, finite relational structure, $\mathbb{D}$, there is an associated decision problem, CSP$(\mathbb{D})$, which is a restricted version of the constraint satisfaction problem. In [8], the so called "algebraic approach" to the…

From any directed graph $E$ one can construct the graph inverse semigroup $G(E)$, whose elements, roughly speaking, correspond to paths in $E$. Wang and Luo showed that the congruence lattice $L(G(E))$ of $G(E)$ is upper-semimodular for…

Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave…

IIn a finite lattice, a congruence spreads from a prime interval to another by a sequence of congruence-perspectivities through \emph{intervals of arbitrary size}, by a 1955 result of J. Jakub\'ik. In this note, I introduce the concept of…

In the recent years a lot of effort has been made to extend the theory of hyperholomorphic functions from the setting of associative Clifford algebras to non-associative Cayley-Dickson algebras, starting with the octonions. An important…

Let A, B, S be categories, let F:A-->S and G:B-->S be functors. We assume that for "many" objects a in A, there exists an object b in B such that F(a) is isomorphic to G(b). We establish a general framework under which it is possible to…

For a finite lattice L, let EL denote the reflexive and transitive closure of the join-dependency relation on L, defined on the set J(L) of all join-irreducible elements of L. We characterize the relations of the form EL, as follows:…

We study quenched SU(N) gauge theories with fermions in the two-index symmetric, antisymmetric and the adjoint representations. Our main motivation is to check whether at large number of colours those theories become non-perturbatively…

Let $\lambda$ and $\kappa$ be cardinal numbers such that $\kappa$ is infinite and either $2\leq \lambda\leq \kappa$, or $\lambda=2^\kappa$. We prove that there exists a lattice $L$ with exactly $\lambda$ many congruences, $2^\kappa$ many…

We give examples of pairs of isotopic algebras with non-isomorphic congruence lattices. This answers the question of whether all isotopic algebras have isomorphic congruence lattices.

In this paper we present a new version of the second author's factorization theorem for perfect matchings of symmetric graphs. We then use our result to solve four open problems of Propp on the enumeration of trimer tilings on the hexagonal…

We study feebly compact shift-continous topologies on the semilattice $\left(\exp_n\lambda,\cap\right)$. It is proved that such $T_1$-topology is sequentially pracompact if and only if it is $\mathfrak{D}(\omega)$-compact.

We prove central limit theorems (CLTs) for topological functionals of Bernoulli bond percolation on infinite graphs beyond the Euclidean lattice $\mathbb{Z}^{d}$. For quasi-transitive graphs of subexponential growth, we show that the number…

We consider two-dimensional lattice equations defined on an elementary square of the Cartesian lattice and depending on the variables at the corners of the quadrilateral. For such equations the property often associated with integrability…

In this paper, we completely classify the isomorphism classes of certain lattices $L_A(C)$ and $L_B(C)$ from a self-orthogonal code $C$ over the finite field $\mathbb{F}_p$, where $p$ is an odd prime. These lattices are obtained by…

We investigate the representation of lattices as sublattices of the lattice of all convex subsets (intervals) of a linearly ordered set $(X,\le)$. We introduce the purely lattice-theoretic notion of a \textit{loc-lattice} and prove that…

We prove the density hypothesis for congruence subgroups of an irreducible uniform lattice in $\mathrm{PSL}_2(\mathbb{R})^d$, extending previous results on the spherical density hypothesis to bound multiplicities of non-tempered…

We prove that for any distributive join-semilattice S, there are a meet-semilattice P with zero and a map f:PxP-->S such that f(x,z)<=f(x,y)vf(y,z) and x<=y implies that f(x,y)=0, for all x,y,z in P, together with the following conditions:…

A distributive lattice structure ${\mathbf M}(G)$ has been established on the set of perfect matchings of a plane bipartite graph $G$. We call a lattice {\em matchable distributive lattice} (simply MDL) if it is isomorphic to such a…

A planar semimodular lattice $K$ is \emph{slim} if $\mathsf{M}_3$ is not a sublattice of~$K$. In a recent paper, G. Cz\'edli found four new properties of congruence lattices of slim, planar, semimodular lattices, including the \emph{No…