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Planar semilattices and nearlattices with eighty-three subnearlattices
Finite (upper) nearlattices are essentially the same mathematical entities as finite semilattices, finite commutative idempotent semigroups, finite...
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Zilber’s Theorem for planar lattices, revisited
Zilber’s Theorem states that a finite lattice L is planar if and only if it has a complementary order relation. We provide a new proof for this...
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One Hundred Twenty-Seven Subsemilattices and Planarity
Let L be a finite n -element semilattice. We prove that if L has at least 127 ⋅ 2 n − 8 subsemilattices, then L is planar. For n > 8, this result is...
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The Number of Subuniverses, Congruences, Weak Congruences of Semilattices Defined by Trees
We determine the number of subuniverses of semilattices defined by arbitrary and special kinds of trees via combinatorial considerations. Using a...
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Semilatice Decompositions of Semigroups. Hereditariness and Periodicity—An Overview
A semigroup is an algebraic structure consisting of a set with an associative binary operation defined on it.Mitrović, Melanija We can say that most...
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On Graphs of Bounded Semilattices
In this paper, we introduce the graph G ( S ) of a bounded semilattice S , which is a generalization of the intersection graph of the substructures of an...
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Geometric Realizations of Tamari Interval Lattices Via Cubic Coordinates
We introduce cubic coordinates, which are integer words encoding intervals in the Tamari lattices. Cubic coordinates are in bijection with...
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\({\mathcal {C}}_1\)-diagrams of slim rectangular semimodular lattices permit quotient diagrams
Slim semimodular lattices (for short, SPS lattices ) and slim rectangular lattices (for short, SR lattices ) were introduced by Grätzer and Knapp (Acta...
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Extracting Persistent Clusters in Dynamic Data via Möbius Inversion
Identifying and representing clusters in time-varying network data is of particular importance when studying collective behaviors emerging in nature,...
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Algebraic Structures and Social Processes
There has long been an interest among social scientists in the use of algebraic structures to analyze social data. Many popular approaches are...
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Historical steps of development of convexity as a field
In this chapter we will show historical steps of the development of convexity as a field and, in addition, developments of the relations between...
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On the number of atoms in three-generated lattices
As the main result of the paper, we construct a three-generated, 2-distributive, atomless lattice that is not finitely presented. Also, the paper...
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Lattices from graph associahedra and subalgebras of the Malvenuto–Reutenauer algebra
The Malvenuto–Reutenauer algebra is a well-studied combinatorial Hopf algebra with a basis indexed by permutations. This algebra contains a wide...
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Idempotents in the Endomorphism Algebra of a Finite Lattice
We give a direct construction of a specific central idempotent in the endomorphism algebra of a finite lattice T . This idempotent is associated with...
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Duality of Graded Graphs Through Operads
Pairs of graded graphs, together with the Fomin property of graded graph duality, are rich combinatorial structures providing among other a framework...
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Zero-divisor Graph Generalizations
The concept of zero-divisor graph has been generalized to many other algebraic structures such as commutative semigroups, noncommutative rings,...
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Solving graph partitioning on sparse graphs: cuts, projections, and extended formulations
This paper explores integer programming formulations for solving graph partitioning problems that impose an upper limit on the weight of the...
