Journal ArticleDOI
The generalized singular direct product for quasigroups
TLDR
In this article, a recursive construction for quasigroups orthogonal to their transposes is given, which is based on the singular direct product (SDP) construction of A. Sade.Abstract:
In [2], A. Sade gives a construction for quasigroups which he calls the singular direct product. In this paper we generalize Sades' construction. As an application we obtain a recursive construction for quasigroups orthogonal to their transposes. All quasigroups considered in this paper will be finite.read more
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Self-orthogonal latin squares of all orders $n \ne 2,3,6$
TL;DR: In this article, it was shown that there exists a self-orthogonal latin square of order n if and only if n 2 9 3, 6 6, 6.
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Cell space approaches in biomathematics
TL;DR: In this paper, the authors explain some principal aspects of various approaches appealing to certain mathematical formulations based upon cell spaces and to illustrate their implications to biomathematics, and summarize their view on the role of biomatahematics which is to be expected to have a certain role different from biophysical consideration.
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Construction of perpendicular steiner quasigroups
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Conjugate orthogonal quasigroups
TL;DR: It is the techniques developed in the disproof of the Euler conjecture which are in fact instrumental in determining the spectrum of conjugate orthogonal quasigroups.
References
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Journal ArticleDOI
Latin squares orthogonal to their transposes
TL;DR: This paper shows how to construct a Latin square orthogonal to its transpose for every order n, such that n ≢ 2 mod 4, or n ≡= 3 mod 9 or n≢ 6 mod 9.