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8  Articles
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We investigate {left, right, middle\} units of quasigroups and families of identities which might imply their existence. A prominent role is played by the newly introduced notion of derivative operation, generalizing Belousov's notions of left/right deriv... see more

Given a binary quasigroup GG of order nn, a dd-iterated quasigroup G[d]G[d] is the (d+1)(d+1)-ary quasigroup equal to the dd-times composition of GG with itself. The Cayley table of every dd-ary quasigroup is a dd-dimensional latin hypercube. Transversals... see more

We prove that a set of v-2 symmetric idempotent latin squares of order v, such that no two of them agree in a off-diagonal position, exists for all odd v>>0. We describe how the techniques used in the proof relate to techniques used in [17] to const... see more

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In a first part, we are concerned with the relationships between polynomials in the two generators of the algebra of Heisenberg—Weyl, its Bargmann—Fock representation with differential operators and the associated one-parameter group.Upon this basis, the ... see more

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