Results 51 to 60 of about 4,967 (212)
, 2008 We characterize the set of all N-ary quasigroups of order 4: every N-ary quasigroup of order 4 is permutably reducible or semilinear. Permutable reducibility means that an N-ary quasigroup can be represented as a composition of K-ary and (N-K+1)-ary ...
Denis S. Krotov +2 more
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Half quasigroups and generalized quasigroup orthogonality
Discrete Mathematics, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Q-Neutrosophic Spherical-Cubic Soft Algebra for Enhancing Residential Space Art Design Courses Quality in IoT-Enabled Smart Factories [PDF]
Neutrosophic Sets and SystemsThis paper introduces a new mathematical model called Q-Neutrosophic Spherical-Cubic Soft Evaluation Algebra (Q-NSCSEA) to support the improvement of educational practices in residential space art design courses. These courses are increasingly integrated
Xiaodan Kong
doaj +1 more source
Asymptotics for the number of n-quasigroups of order 4
, 2006 The asymptotic form of the number of n-quasigroups of order 4 is $3^{n+1} 2^{2^n +1} (1+o(1))$.
D. S. Krotov +4 more
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Journal of Algebra, 1996 It is well known that the following four Moufang identities, M1: \((x(yz))x=(xy)(zx)\) and N1: \(((xy)z)y=x(y(zy))\) and their respective mirrors M2 and N2 (obtained by writing them backwards), are equivalent in loops which are then called Moufang loops. The author now shows that every quasigroup satisfying any one of these four identities is a Moufang
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Efficient Quasigroup Block Cipher for Sensor Networks [PDF]
International Conference on Computer Communications and Networks, 2012 We present a new quasigroup based block encryption system with and without cipher-block-chaining. We compare its performance against Advanced Encryption Standard-256 (AES256) bit algorithm using the NIST statistical test suite (NIST-STS) that tests for ...
Matthew Battey, Abhishek Parakh
semanticscholar +1 more source
Mathematica Slovaca, 2011 Abstract Napoleon’s quasigroups are idempotent medial quasigroups satisfying the identity (ab·b)(b·ba) = b. In works by V. Volenec geometric terminology has been introduced in medial quasigroups, enabling proofs of many theorems of plane geometry to be carried out by formal calculations in a quasigroup.
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Commuting Pairs in Quasigroups
Journal of Combinatorial Designs, Volume 33, Issue 11, Page 418-427, November 2025.ABSTRACT A quasigroup is a pair ( Q , ∗ ), where Q is a nonempty set and ∗ is a binary operation on Q such that for every ( a , b ) ∈ Q 2, there exists a unique ( x , y ) ∈ Q 2 such that a ∗ x = b = y ∗ a. Let ( Q , ∗ ) be a quasigroup. A pair ( x , y ) ∈ Q 2 is a commuting pair of ( Q , ∗ ) if x ∗ y = y ∗ x.
Jack Allsop, Ian M. Wanless
wiley +1 more source
Dynamical Yang-Baxter Maps with an Invariance Condition
, 2007 By means of left quasigroups L=(L, .) and ternary systems, we construct dynamical Yang-Baxter maps associated with L, L, and (.) satisfying an invariance condition that the binary operation (.) of the left quasigroup L defines.
Shibukawa, Youichi
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Canonical Labeling of Latin Squares in Average‐Case Polynomial Time
Random Structures &Algorithms, Volume 66, Issue 4, July 2025.ABSTRACT A Latin square of order n$$ n $$ is an n×n$$ n\times n $$ matrix in which each row and column contains each of n$$ n $$ symbols exactly once. For ε>0$$ \varepsilon >0 $$, we show that with high probability a uniformly random Latin square of order n$$ n $$ has no proper subsquare of order larger than n1/2log1/2+εn$$ {n}^{1/2}{\log}^{1/2 ...
Michael J. Gill +2 more
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