Displaying similar documents to “Travel groupoids on infinite graphs”

Travel groupoids

Ladislav Nebeský (2006)

Czechoslovak Mathematical Journal

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In this paper, by a travel groupoid is meant an ordered pair ( V , * ) such that V is a nonempty set and * is a binary operation on V satisfying the following two conditions for all u , v ∈ V : ( u * v ) * u = u ; if ( u * v ) * v = u , then u = v . Let ( V , * ) be a travel groupoid. It is easy to show that if x , y ∈ V , then x * y = y if and only if y * x = x . We say that ( V , * ) is on a (finite or infinite) graph G if V ( G ) = V and E ( G ) = { { u , v } u , v ∈ V and u ≠ u * v = v } . Clearly, every travel groupoid is on exactly one graph. In this paper, some properties of travel groupoids on graphs are studied.

Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs

Ilwoo Cho, Palle E. T. Jorgensen (2015)

Special Matrices

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In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the algebra A of all arithmetic functions, we establish a corresponding subalgebra AG = C*[α(G)]︀ of A. We construct a suitable representation of AG, determined both by G and by an arbitrarily fixed prime p. And then based on this representation,...

Completely dissociative groupoids

Milton Braitt, David Hobby, Donald Silberger (2012)

Mathematica Bohemica

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In a groupoid, consider arbitrarily parenthesized expressions on the k variables x 0 , x 1 , ⋯ x k - 1 where each x i appears once and all variables appear in order of their indices. We call these expressions k -ary formal products, and denote the set containing all of them by F σ ( k ) . If u , v ∈ F σ ( k ) are distinct, the statement that u and v are equal for all values of x 0 , x 1 , ⋯ x k - 1 is a generalized associative law. Among other results, we show that many small groupoids are completely dissociative, meaning that no generalized associative...

Canonical Objects in Classes of (n, V)-Groupoids

Celakoska-Jordanova, Vesna (2010)

Mathematica Balkanica New Series

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AMS Subj. Classification: 03C05, 08B20 Free algebras are very important in studying classes of algebras, especially varieties of algebras. Any algebra that belongs to a given variety of algebras can be characterized as a homomorphic image of a free algebra of that variety. Describing free algebras is an important task that can be quite complicated, since there is no general method to resolve this problem. The aim of this work is to investigate classes of groupoids, i.e. algebras...