Related papers: Lattice tolerances and congruences
We formalize the concept of a centralizer-respecting homomorphism, surjective homomorphisms which are equivariant with respect to taking the centralizer of a subgroup. There is a functor from the category of centralizer-respecting…
We find (completeness type) conditions on topological semilattices $X,Y$ guaranteeing that each continuous homomorphism $h:X\to Y$ has closed image $h(X)$ in $Y$.
We present some identities dealing with reflexive and admissible relations and which, through a variety, are equivalent to congruence modularity.
For a finite lattice $\Lambda$, $\Lambda$-ultrametric spaces have, among other reasons, appeared as a means of constructing structures with lattices of equivalence relations embedding $\Lambda$. This makes use of an isomorphism of…
We show that the set of all measures on any measurable space is a complete lattice, i.e. every collection of measures has both a greatest lower bound and a least upper bound.
In a 1998 paper with H. Lakser, the authors proved that every finite distributive lattice $D$ can be represented as the congruence lattice of a finite \emph{semimodular lattice}. Some ten years later, the first author and E. Knapp proved a…
We prove several rigorous results about the asymptotic behaviour of the numbers of tadpoles (or lassos) embedded in a lattice, including cases where the head is subject to a constraint like being unknotted, or where the tail pierces the…
We compare, for the static potential and at short distances, perturbation theory with the results of lattice simulations. We show that a renormalon-dominance picture explains why in the literature sometimes agreement, and another…
We characterize factor congruences in semilattices by using generalized notions of order ideal and of direct sum of ideals. When the semilattice has a minimum (maximum) element, these generalized ideals turn into ordinary (dual) ideals.
We review principal results on axiomatizability of classes of lattices of equivalences
Motivated by Kohno's result on the holonomy Lie algebra of a hyperplane arrangement, we define the holonomy Lie algebra of a finite geometric lattice in a combinatorial way. For a solvable pair of lattices, we show that the holonomy Lie…
Every lattice is isomorphic to a lattice whose elements are sets of sets, and whose operations are intersection and an operation extending the union of two sets of sets A and B by the set of all sets in which the intersection of an element…
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This subclass of perfect graphs has been extensively studied, due to both its interesting structure…
An interesting application of the gauge/gravity duality to condensed matter physics is the description of a lattice via breaking translational invariance on the gravity side. By making use of global symmetries, it is possible to do so…
We show that the threshold of complete synchronization in a lattice of coupled non-smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace. We examine carefully the…
We give a shorter and simpler proof of the result of [2], which gives a necessary and sufficient condition for when a lattice diagram is the projection of a lattice link.
Diversities are a generalization of metric spaces, where instead of the non-negative function being defined on pairs of points, it is defined on arbitrary finite sets of points. Diversities have a well-developed theory. This includes the…
Coherence simplices are generic topological correlation-function defects supported by a hierarchy of coherence functions. We classify coherence simplices based on their topology and discuss their structure and dynamics, together with their…
We consider interface fluctuations on a two-dimensional layered lattice where the couplings follow a hierarchical sequence. This problem is equivalent to the diffusion process of a quantum particle in the presence of a one-dimensional…
In this article, we investigate the status of the homomorphism preservation property amongst restricted classes of finite relational structures and algebraic structures. We show that there are many homomorphism-closed classes of finite…