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Partitioned binary relations [PDF]

MATHEMATICA SCANDINAVICA, 2011
We define the category of partitioned binary relations and show that it contains many classical diagram categories, including categories of binary relations, maps, injective maps, partitions, (oriented) Brauer diagrams and (oriented) Temperley-Lieb diagrams.
Paul Martin, Volodymyr Mazorchuk
semanticscholar   +7 more sources

A theorem on the semigroup of binary relations [PDF]

Proceedings of the American Mathematical Society, 1969
PROOF. Necessity. Let p =p5p, where 5 ESx. Let o = 6p, then o2 = andp =po-. It is known in [1] that L(of) and L(p) are complete lattices in which joins are unions and, moreover, L(of) is completely distributive. If A CX, then it is easy to show that {t(A) =4t(4(A)) and +(A) =x(+1(A)) where c(A)EL(o-), ql(A)EL(p) and X(A)EL(a). Define the mapping 0 of L(
Jaw-ching Yang
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Binary and ternary relations [PDF]

Mathematica Bohemica, 1992
Let \(G\) be a set, \(\rho\) a binary relation on \(G\). Further, let \(r\) be a binary relation on the set \(\rho\) with the property \(\alpha=(x,y)\in\rho\), \(\beta=(z,u)\in\rho\), \((\alpha,\beta)\in r\Rightarrow y=z\). Then \(r\) is called a binding relation on \(\rho\), and \((G,\rho,r)\) is called a double binary structure.
Vítězslav Novák, Miroslav Novotný
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On Some Properties of Binary Relations [PDF]

Nagoya Mathematical Journal, 1957
Some important notions in the theory of binary relations such as the relative product of two relations and the converse of a relation are defined in Whitehead and Russell’s “Principia mathematica” ([1]). McKinsey ([2]) and Tarski ([3]) gave their systems of postulates for the calculus of relations.
Katuzi Ono
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Selective Games on Binary Relations [PDF]

Topology and its Applications, 2014
We present a unified approach, based on dominating families in binary relations, for the study of topological properties defined in terms of selection principles and the games associated to them.Comment: 28 ...
Dias, Rodrigo R., Scheepers, Marion
core   +4 more sources

A note on first-order spectra with binary relations [PDF]

Logical Methods in Computer Science, 2018
The spectrum of a first-order sentence is the set of the cardinalities of its finite models. In this paper, we consider the spectra of sentences over binary relations that use at least three variables.
Eryk Kopczynski, Tony Tan
doaj   +3 more sources

Distributivity of lattices of binary relations [PDF]

Mathematica Bohemica, 2002
Summary: We present a formal scheme which, whenever satisfied by relations of a given relational lattice \(L\) containing only reflexive and transitive relations, ensures distributivity of \(L\).
Ivan Chajda
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Binary relations and reduced hypergroups

Discrete Mathematics, 2007
AbstractDifferent partial hypergroupoids are associated with binary relations defined on a set H. In this paper we find sufficient and necessary conditions for these hypergroupoids in order to be reduced hypergroups. Given two binary relations ρ and σ on H we investigate when the hypergroups associated with the relations ρ∩σ, ρ∪σ and ρσ are reduced. We
Irina Cristea, Mirela Ştefănescu
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A construction for idempotent binary relations [PDF]

Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1970
Boris M. Schein
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Induction on fields of binary relations. [PDF]

Notre Dame Journal of Formal Logic, 1972
W. Russell Belding
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