Related papers: Strongly modular lattices with long shadow

For some important families of complete infinite lattices, we study some generalizations of two fundamental notions which are mostly treated for finite lattices. Specifically, for well-separated $\kappa$-lattices, and also for weakly atomic…

For a modular lattice $L$ of finite length, we prove that the distributivity of $L$ is a sufficient condition while its 2-distributivity is a necessary condition that those sublattices of $L$ that are closed under taking relative…

We completely determine all lower-modular elements of the lattice of all semigroup varieties. As a corollary, we show that a lower-modular element of this lattice is modular.

A lattice L is slim if it is finite and the set of its join-irreducible elements contains no three-element antichain. Slim, semimodular lattices were previously characterized by G. Cz\'edli and E.T. Schmidt as the duals of the lattices…

Patch lattices, introduced by G. Cz\'edli and E.T. Schmidt in 2013, are the building stones for slim (and so necessarily finite and planar) semimodular lattices with respect to gluing. Slim semimodular lattices were introduced by G.…

For two subsets S and T of a given lattice L, we define a relative distributive (modular) property over L, that underlies a large family including the usual class of distributive (modular) lattices. Our proposed class will be called…

We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.

We study maximal sublattices of finite semidistributive lattices via their complements. We focus on the conjecture that such complements are always intervals, which is known to be true for bounded lattices. Since the class of…

We classify the unimodular equivalence classes of inclusion-minimal polygons with a certain fixed lattice width. As a corollary, we find a sharp upper bound on the number of lattice points of these minimal polygons.

We introduce and study the category of modular (i.e. with coefficient of positive characteristic) monodromic perverse sheaves on complex stratified $T$-varieties, with $T$ a complex algebraic torus. In particular, we show that under…

We consider the lattice of coarse structures on a set $X$ and study metrizable, locally finite and cellular coarse structures on $X$ from the lattice point of view.

Matrices over the dual numbers are considered. We propose an approach to classify these matrices up to similarity. Some preliminary results on the realization of this approach are obtained. In particular, we produce explicitly canonical…

We study weaker variations of the property of flatness in matroid theory. We show that these variations form a chain of increasingly stronger properties all implying pseudomodularity on its lattice of flats. We show examples in the gammoid…

In this paper, we present a simple lattice-theoretic characterization for affine buildings of type A. We introduce a class of modular lattices, called uniform modular lattices, and show that uniform modular lattices and affine buildings of…

We study the model theoretic strength of various lattices that occur naturally in topology, like closed (semi-linear or semi-algebraic or convex) sets. The method is based on weak monadic second order logic and sharpens previous results by…

We consider posets of lattice paths (endowed with a natural order) and begin the study of such structures. We give an algebraic condition to recognize which ones of these posets are lattices. Next we study the class of Dyck lattices (i.e.,…

Representing lattices L by equivalence relations amounts to embed them into the lattice Part(V) of all partitions of a set V, and has a long history. Here we are concerned with MODULAR lattices L and aim for sets V as small as possible,…

Let $\Lambda$ be a basic finite dimensional algebra over an algebraically closed field, presented as a path algebra modulo relations; further, assume that $\Lambda$ is graded by lengths of paths. The paper addresses the classifiability, via…

We force the existence of a chain of length $\omega_3$ in $[\omega_1]^{\omega_1}$ increasing modulo finite. The construction involves symmetric systems of models of two types as side conditions, introduced by the second author. This…

We introduce two classes of discrete polynomials and construct discrete equations admitting a Lax representation in terms of these polynomials. Also we give an approach which allows to construct lattice integrable hierarchies in its…