Related papers: A broad class of shellable lattices
In this article, we first characterize pseudocomplemented inductive modular lattices by using their two 0-sublattices. Then we use two 0-sublattices of a subgroup lattice to describe all locally cyclic abelian groups. In particular, we show…
Imposing a strong condition on the linear order of shellable complexes, we introduce strong shellability. Basic properties, including the existence of dimension-decreasing strong shelling orders, are developed with respect to nonpure…
We provide a direct proof that a finite graded lattice with a maximal chain of left modular elements is supersolvable. This result was first established via a detour through EL-labellings in [McNamara-Thomas] by combining results of…
This paper investigates the theory of lattices, focusing on extending lattices relative to abstract classes, modular lattices, and torsion lattices. Definitions of type-1 and type-2 extending lattices are provided, along with their weakly…
We initiate an investigation of lattices in a new class of locally compact groups, so called locally pro-$p$-complete Kac-Moody groups. We discover that in rank 2 their cocompact lattices are particularly well-behaved: under mild…
This article focuses on the relationship between pseudo-t-norms and the structure of lattices. First, we establish a necessary and sufficient condition for the existence of a left-continuous t-norm on the ordinal sum of two disjoint…
We are interested in expanding our understanding of symplectic matroids by exploring the properties of a class of symplectic matroids with a "lattice of flats". Taking a well-behaved family of subdivisions of the cross polytope we obtain a…
The $\gamma$-Cambrian semilattices $\mathcal{C}_{\gamma}$ defined by Reading and Speyer are a family of meet-semilattices associated with a Coxeter group $W$ and a Coxeter element $\gamma\in W$, and they are lattices if and only if $W$ is…
A mixed lattice is a partially ordered set with two mixed partial orderings that are linked by asymmetric upper and lower envelopes. These notions generalize the join and meet operations of a lattice. In the present paper, we study…
The congruence lattices of all algebras defined on a fixed finite set $A$ ordered by inclusion form a finite atomistic lattice $\mathcal E$. We describe the atoms and coatoms. Each meet-irreducible element of $\mathcal E$ being determined…
Geometric lattices are characterized in this paper as those finite, atomic lattices such that every atom ordering induces a lexicographic shelling given by an edge labeling known as a minimal labeling. Equivalently, geometric lattices are…
We introduce the notion of compactifiable classes -- these are classes of metrizable compact spaces that can be up to homeomorphic copies ``disjointly combined'' into one metrizable compact space. This is witnessed by so-called compact…
We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type $D_n$ and those of exceptional type and rank…
We classify t-structures and thick subcategories in discrete cluster categories $\mathcal{C}(\mathcal{Z})$ of Dynkin type $A$, and show that the set of all t-structures on $\mathcal{C}(\mathcal{Z})$ is a lattice under inclusion of aisles,…
Let $L$ be a planar semimodular lattice. We call $L$ \emph{slim}, if it has no $\mthree$ sublattice. Let us define an \emph{SPS lattice} as a slim, planar, semimodular lattice $L$. In 2016, I proved a property of congruences of SPS lattices…
The set of all cancellable elements of the lattice of semigroup varieties has recently been shown to be countably infinite. But the description of all cancellable elements of the lattice $\mathbb{MON}$ of monoid varieties remains unknown.…
This paper explores alternative statements of the axioms for lattice gluing, focusing on lattices that are modular, locally finite, and have finite covers, but may have infinite height. We give a set of "maximal" axioms that maximize what…
One-dimensional quasilattices are classified into mutual local-derivability (MLD) classes on the basis of geometrical and number-theoretical considerations. Most quasilattices are ternary, and there exist an infinite number of MLD classes.…
With a complete residuated lattice $L$ as the truth value table, we extend the definition of sobriety of classical convex spaces to the framework of $L$-convex spaces. We provide a specific construction for the sobrification of an…
Implicational bases are a well-known representation of closure spaces and their closure lattices. This representation is not unique, though, and a closure space usually admits multiple bases. Among these, the canonical base, the canonical…