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pro vyhledávání: '"Allsop, Jack"'
Autor:
Allsop, Jack, Wanless, Ian M.
A quasigroup is a pair $(Q, *)$ where $Q$ is a non-empty set and $*$ is a binary operation on $Q$ such that for every $(a, b) \in Q^2$ there exists a unique $(x, y) \in Q^2$ such that $a*x=b=y*a$. Let $(Q, *)$ be a quasigroup. A pair $(x, y) \in Q^2$
Externí odkaz:
http://arxiv.org/abs/2412.08107
Autor:
Allsop, Jack, Wanless, Ian M.
We prove that with probability $1-o(1)$ as $n \to \infty$, a uniformly random Latin square of order $n$ contains no subsquare of order $4$ or more, resolving a conjecture of McKay and Wanless. We also show that the expected number of subsquares of or
Externí odkaz:
http://arxiv.org/abs/2409.08446
Autor:
Allsop, Jack, Wanless, Ian M.
A $d$-dimensional Latin hypercube of order $n$ is a $d$-dimensional array containing symbols from a set of cardinality $n$ with the property that every axis-parallel line contains all $n$ symbols exactly once. We show that for $(n, d) \notin \{(4,2),
Externí odkaz:
http://arxiv.org/abs/2310.01923
Autor:
Allsop, Jack
Publikováno v:
J. Combin. Des. 31, (2023), 447-475
A Latin square of order $n$ is an $n \times n$ matrix of $n$ symbols, such that each symbol occurs exactly once in each row and column. For an odd prime power $q$ let $\mathbb{F}_q$ denote the finite field of order $q$. A quadratic Latin square is a
Externí odkaz:
http://arxiv.org/abs/2302.12942
Autor:
Allsop, Jack, Wanless, Ian M.
Publikováno v:
Proc. London Math. Soc. (3) 128 (2024), e12575
A \emph{Latin square} is a matrix of symbols such that each symbol occurs exactly once in each row and column. A Latin square $L$ is \emph{row-Hamiltonian} if the permutation induced by each pair of distinct rows of $L$ is a full cycle permutation. R
Externí odkaz:
http://arxiv.org/abs/2211.13826
Autor:
Allsop, Jack, Wanless, Ian M.
Publikováno v:
Finite Fields Appl. 75 (2021), 101893
An orthomorphism over a finite field $\mathbb{F}_q$ is a permutation $\theta:\mathbb{F}_q\mapsto\mathbb{F}_q$ such that the map $x\mapsto\theta(x)-x$ is also a permutation of $\mathbb{F}_q$. The degree of an orthomorphism of $\mathbb{F}_q$, that is,
Externí odkaz:
http://arxiv.org/abs/2103.02153
Akademický článek
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Autor:
Allsop, Jack
Publikováno v:
Journal of Combinatorial Designs; Sep2023, Vol. 31 Issue 9, p447-475, 29p
