Self-orthogonal cyclic n-quasigroups.
Self-orthogonal cyclic n-quasigroups. (Short Communication).
Sequenceable groups and related topics.
Signatura of magic and Latin integer squares: isentropic clans and indexing
The 2010 study of the Shannon entropy of order nine Sudoku and Latin square matrices by Newton and DeSalvo [Proc. Roy. Soc. A 2010] is extended to natural magic and Latin squares up to order nine. We demonstrate that decimal and integer measures of the Singular Value sets, here named SV clans, are a powerful way of comparing different integer squares. Several complete sets of magic and Latin squares are included, including the order eight Franklin subset which is of direct relevance...
Six little squares and how their numbers grow.
Sofic groups are not locally embeddable into finite Moufang loops
We shall show that there exist sofic groups which are not locally embeddable into finite Moufang loops. These groups serve as counterexamples to a problem and two conjectures formulated in the paper by M. Vodička, P. Zlatoš (2019).
Solution of distributive-like quasigroup functional equations
We are investigating quasigroup functional equation classification up to parastrophic equivalence [Sokhatsky F.M.: On classification of functional equations on quasigroups, Ukrainian Math. J. 56 (2004), no. 4, 1259–1266 (in Ukrainian)]. If functional equations are parastrophically equivalent, then their functional variables can be renamed in such a way that the obtained equations are equivalent, i.e., their solution sets are equal. There exist five classes of generalized distributive-like quasigroup...
Some new optimum Golomb rectangles.
Subfield permutation polynomials and orthogonal subfield systems in finite fields