Results 101 to 110 of about 998 (166)
Varieties of Hexagonal Quasigroups
Journal of Algebra, 1993 The decomposition of a complete graph into disjoint cycles can be used to define a binary operation \(\star\) on the vertices of the graph -- if a cycle is \((\dots, a, b, c, \dots)\) then \(a \star b = c\) and \(c \star b = a\). In general the groupoid thus obtained is not a quasigroup, but when the decomposition satisfies an extra condition, known as
openaire +2 more sources
Symmetries in hexagonal quasigroups [PDF]
Archivum Mathematicum, 2007 Hexagonal quasigroup is idempotent medial and semisymmetric quasigroup. In this article we define and study symmetries about a point, segment and ordered triple of points in hexagonal quasigroups. The main results are the theorems on composition of two and three symmetries.
Volenec, Vladimir, Bombardelli, Mea
openaire +2 more sources
A class of distributive quasigroup and its parastrophs
, 2021 Given a quasigroup (Q ;), there exist five other associated quasigroups which are called its parastrophs. In this paper, the parastrophic invariance of a left-right sided quasigroup (Q ;) is investigated.
Ajala, S.O. +3 more
core
Quasigroup String Transformations and Hash Function Design
, 2010 In this paper we propose two new types of compression functions, based on quasigroup string transformations. The first type uses known quasigroup string transformations, defined elsewhere, by changing alternately the transformation direction, going ...
Markovski, Smile, Mileva, Aleksandra
core +2 more sources
On a quasigroup prolongation and its recursive differentiability
Acta et Commentationes: Ştiinţe Exacte şi ale NaturiiWe consider a method of quasigroups prolongation by adding two new elements and by using two transversals that intersect in exactly one cell. In a Latin square L of order q, along with usual transversals we call "free transversals" any set of q cells ...
Elena Cuznețov
doaj +1 more source
SAC loops and loops of order five
Математика, інформатика, фізика: наука та освітаIn this article, we continue the analytical research of small-order loops. Namely, we investigate loops of order 5. Recall that an element of a loop is called unipotent if its square is neutral.
Fedir Sokhatsky
doaj +1 more source
A Note on the Quasigroup of Lai–Massey Structures
CryptographyIn our paper, we explore the consequences of replacing the commutative group operation used in Lai–Massey structures with a quasigroup operation. We introduce four quasigroup versions of the Lai–Massey structure and prove that for quasigroups isotopic ...
George Teşeleanu
doaj +1 more source
Arc Consistency and Quasigroup Completion
, 1998 Quasigroup completion is a recently proposed benchmark constraint satisfaction problem that combines the features of randomly generated instances and highly structured problems.
Paul Shaw, Toby Walsh, Kostas Stergiou
core
Sub-quasigroups of finite quasigroups [PDF]
Pacific Journal of Mathematics, 1957 openaire +2 more sources
Classification of quasigroup functional equations and identities of minimal length.
, 2019 Classification of quasigroup functional equations and identities of minimal ...
Krainichuk, H.
core