Related papers: Decomposition theorem on matchable distributive la…

Following G. Gr\"atzer and E. Knapp (2007), a slim semimodular lattice, SPS lattice for short, is a finite planar semimodular lattice having no $M_3$ as a sublattice. An SPS lattice is a slim rectangular lattice if it has exactly two doubly…

Let $G$ be a finite group, and let $\Delta(G)$ be the prime graph built on the set of conjugacy class sizes of $G$: this is the simple undirected graph whose vertices are the prime numbers dividing some conjugacy class size of $G$, two…

We give a complete characterization of bipartite graphs having tree-like Galois lattices. We prove that the poset obtained by deleting bottom and top elements from the Galois lattice of a bipartite graph is tree-like if and only if the…

For a rank two root system and a pair of nonnegative integers, using only elementary combinatorics we construct two posets. The constructions are uniform across the root systems A1+A1, A2, C2, and G2. Examples appear in Figures 3.2 and 3.3.…

We investigate an integrable property and observables of 2 dimensional N=(4,4) topological field theory defined on a discrete lattice by using the "orbifolding" and "deconstruction" methods. We show that our lattice model possesses the…

We define when a ternary term $m$ of an algebraic language $\mathcal{L}$ is called a \textit{distributive nearlattice term} (DN-term) of a sentential logic $\mathcal{S}$. Distributive nearlattices are ternary algebras generalising Tarski…

De Morgan bisemilattices are expansions of distributive bisemilattices by an involution satisfying De Morgan properties. They have attracted interest both as algebraic models of analytic containment logics, and as a case study for a certain…

Let $G$ be an acylic directed graph. For each vertex $g \in G$, we define an involution on the independent sets of $G$. We call these involutions flips, and use them to define a new partial order on independent sets of $G$. Trim lattices…

It is argued in (Eklund et al., 2018) that the quantale [L,L] of sup-preserving endomaps of a complete lattice L is a Girard quantale exactly when L is completely distributive. We have argued in (Santocanale, 2020) that this Girard quantale…

We prove the following version of the Loebl-Komlos-Sos Conjecture: For every alpha>0 there exists a number M such that for every k>M every n-vertex graph G with at least (0.5+alpha)n vertices of degree at least (1+alpha)k contains each tree…

In this article, we continue the study of monadic distributive lattices (or m-lattices) which are a natural generalization of monadic Heyting algebras, introduced by Monteiro and Varsavsky and developed exhaustively by Bezhanishvili. First,…

An instance of a strongly stable matching problem (SSMP) is an undirected bipartite graph $G=(A \cup B, E)$, with an adjacency list of each vertex being a linearly ordered list of ties, which are subsets of vertices equally good for a given…

We introduce the dimension monoid of a lattice L, denoted by Dim L. The monoid Dim L is commutative and conical, the latter meaning that the sum of any two nonzero elements is nonzero. Furthermore, Dim L is given along with the dimension…

A partial lattice P is ideal-projective, with respect to a class C of lattices, if for every K $\in$ C and every homomorphism $\phi$ of partial lattices from P to the ideal lattice of K, there are arbitrarily large choice functions f : P…

In this paper, a question due to Heckenberger, Shareshian and Welker on racks in [7] is positively answered. A rack is a set together with a selfdistributive bijective binary operation. We show that the lattice of subracks of every finite…

We prove a general categorical theorem that enables us to state that under certain conditions, the range of a functor is large. As an application, we prove various results of which the following is a prototype: If every diagram, indexed by…

A partial algebra construction of Gr\"atzer and Schmidt from "Characterizations of congruence lattices of abstract algebras" (Acta Sci. Math. (Szeged) 24 (1963), 34-59) is adapted to provide an alternative proof to a well-known fact that…

This article is part of my upcoming masters thesis which investigates the following open problem from the book, Free Lattices, by R.Freese, J.Jezek, and J.B. Nation published in 1995: "Which lattices (and in particular which countable…

In matching theory, one of the most fundamental and classical branches of combinatorics, {\em canonical decompositions} of graphs are powerful and versatile tools that form the basis of this theory. However, the abilities of the known…

In an earlier paper by three of the present authors and Csaba Schneider, it was shown that, for $m\ge2$, a set of $m+1$ partitions of a set $\Omega$, any $m$ of which are the minimal non-trivial elements of a Cartesian lattice, either form…