--quasigroups.
Generalized distributivity equation on GD-groupoids
Generalized entropy on GD-groupoids with applications to quasigroups of various arities
Generalized graph cordiality
Hovey introduced A-cordial labelings in [4] as a simultaneous generalization of cordial and harmonious labelings. If A is an abelian group, then a labeling f: V(G) → A of the vertices of some graph G induces an edge-labeling on G; the edge uv receives the label f(u) + f(v). A graph G is A-cordial if there is a vertex-labeling such that (1) the vertex label classes differ in size by at most one and (2) the induced edge label classes differ in size by at most one. Research on A-cordiality...
Generating quasigroups for cryptographic applications
A method of generating a practically unlimited number of quasigroups of a (theoretically) arbitrary order using the computer algebra system Maple 7 is presented. This problem is crucial to cryptography and its solution permits to implement practical quasigroup-based endomorphic cryptosystems. The order of a quasigroup usually equals the number of characters of the alphabet used for recording both the plaintext and the ciphertext. From the practical viewpoint, the most important quasigroups are of...
Geodesic loops.
Global left loop structures on spheres
On the unit sphere in a real Hilbert space , we derive a binary operation such that is a power-associative Kikkawa left loop with two-sided identity , i.e., it has the left inverse, automorphic inverse, and properties. The operation is compatible with the symmetric space structure of . is not a loop, and the right translations which fail to be injective are easily characterized. satisfies the left power alternative and left Bol identities “almost everywhere” but not everywhere....
Golden section quasigroups as special idempotent medial quasigroups
Groupoids and the associative law I. (Associative triples)
Groupoids and the associative law II. (Groupoids with small semigroup distance)
Groupoids and the associative law III. (Szász-Hájek groupoids)
Groupoids and the associative law IIIA. (Primitive extensions of SH-groupoids and their semigroup distances)
Groupoids and the associative law IV. (Szász-Hájek Groupoids of Type (A, B, A))
Groupoids and the associative law V. (Szász-Hájek groupoids fo type (A, A, B))
Groupoids and the associative law. VII. Semigroup distance of SH-groupoids
Groupoids and the associative law VIIA. (SH-groupoids of type (A, B, A) and their semigroup distances)
Groupoids and the associative law XII. (Representable cardinal functions)
Groups, transversals, and loops
A family of loops is studied, which arises with its binary operation in a natural way from some transversals possessing a ``normality condition''.
Grupoids and the associative law VII B (SH-grupoids and simply generated congruences)
GS-quasigroups