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Reading Mathematical Texts with Structuralist Semiotics
In this chapter, we use structuralist semiotics as a framework for analyzing mathematical textual practices. We begin with a short introduction, in...
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Growth of k-Dimensional Systoles in Congruence Coverings
We study growth of absolute and homological k -dimensional systoles of arithmetic n -manifolds along congruence coverings. Our main interest is in the...
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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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Reading Mathematical Texts with Structuralist Semiotics
In this chapter, we use structuralist semiotics as a framework for analyzing mathematical textual practices. We begin with a short introduction, in...
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Topological Aspects of Granular Computing
Granular computing is an area of theoretical computer science which is highly useful in nature. Recently, several new directions of granular...
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Solids
To the notion of the dihedral corresponds, in plane geometry, that of the usual angle. This is emphasized also with the next definition which gives...
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The structure of completely meet irreducible congruences in strongly Fregean algebras
A strongly Fregean algebra is an algebra such that the class of its homomorphic images is Fregean and the variety generated by this algebra is...
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Celebrating Loday’s associahedron
We survey Jean-Louis Loday’s vertex description of the associahedron, and its far reaching influence in combinatorics, discrete geometry, and...
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Slim patch lattices as absolute retracts and maximal lattices
We prove that slim patch lattices are exactly the absolute retracts with more than two elements for the category of slim semimodular lattices with...
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The topological shadow of \({{{\mathbb {F}}}_1}\)-geometry: congruence spaces
In this paper we introduce congruence spaces, which are topological spaces that are canonically attached to monoid schemes and that reflect closed...
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Pointed Lattice Subreducts of Varieties of Residuated Lattices
We study the pointed lattice subreducts of varieties of residuated lattices (RLs) and commutative residuated lattices (CRLs), i.e. lattice subreducts...
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