• 제목/요약/키워드: travel groupoid

검색결과 2건 처리시간 0.015초

CHARACTERIZATION OF TRAVEL GROUPOIDS BY PARTITION SYSTEMS ON GRAPHS

  • Cho, Jung Rae;Park, Jeongmi
    • East Asian mathematical journal
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    • 제35권1호
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    • pp.17-22
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    • 2019
  • A travel groupoid is a pair (V, ${\ast}$) of a set V and a binary operation ${\ast}$ on V satisfying two axioms. For a travel groupoid, we can associate a graph in a certain manner. For a given graph G, we say that a travel groupoid (V, ${\ast}$) is on G if the graph associated with (V, ${\ast}$) is equal to G. There are some results on the classification of travel groupoids which are on a given graph [1, 2, 3, 9]. In this article, we introduce the notion of vertex-indexed partition systems on a graph, and classify the travel groupoids on the graph by the those vertex-indexed partition systems.

THE SEMIGROUPS OF BINARY SYSTEMS AND SOME PERSPECTIVES

  • Kim, Hee-Sik;Neggers, Joseph
    • 대한수학회보
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    • 제45권4호
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    • pp.651-661
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    • 2008
  • Given binary operations "*" and "$\circ$" on a set X, define a product binary operation "$\Box$" as follows: $x{\Box}y\;:=\;(x\;{\ast}\;y)\;{\circ}\;(y\;{\ast}\;x)$. This in turn yields a binary operation on Bin(X), the set of groupoids defined on X turning it into a semigroup (Bin(X), $\Box$)with identity (x * y = x) the left zero semigroup and an analog of negative one in the right zero semigroup (x * y = y). The composition $\Box$ is a generalization of the composition of functions, modelled here as leftoids (x * y = f(x)), permitting one to study the dynamics of binary systems as well as a variety of other perspectives also of interest.