One-Sided Quantum Quasigroups and Loops

Right Product Quasigroups and Loops

Right groups are direct products of right zero semigroups and groups and they play a significant role in the semilattice decomposition theory of semigroups. Right groups can be characterized as associative right quasigroups (magmas in which left translations are bijective). If we do not assume associativity we get right quasigroups which are not necessarily representable as direct products of r...

Small Latin Squares, Quasigroups and Loops

We present the numbers of isotopy classes and main classes of Latin squares, and the numbers of isomorphism classes of quasigroups and loops, up to order 10. The best previous results were for Latin squares of order 8 (Kolesova, Lam and Thiel, 1990), quasigroups of order 6 (Bower, 2000) and loops of order 7 (Brant and Mullen, 1985). The loops of order 8 have been independently found by “QSCGZ” ...

Fooling One-Sided Quantum Protocols

We use the venerable “fooling set” method to prove new lower bounds on the quantum communication complexity of various functions. Let f : X × Y → {0, 1} be a Boolean function, fool1(f) its maximal fooling set size among 1-inputs, Q1(f) its one-sided-error quantum communication complexity with prior entanglement, and NQ(f) its nondeterministic quantum communication complexity (without prior enta...

Isotopy Theory Of Smarandache : Quasigroups And Loops ∗ †

The concept of Smarandache isotopy is introduced and its study is explored for Smarandache: groupoids, quasigroups and loops just like the study of isotopy theory was carried out for groupoids, quasigroups and loops. The exploration includes: Smarandache; isotopy and isomorphy classes, Smarandache f, g principal isotopes and G-Smarandache loops.

Computing with quasigroups and loops in GAP