Zobrazeno 1 - 10
of 4 825
pro vyhledávání: '"Wanless, A."'
Autor:
Ghafari, Afsane, Wanless, Ian M.
We prove that, for all even $n\geq10$, there exists a latin square of order $n$ with at least one transversal, yet all transversals coincide on $ \big\lfloor n/6 \big\rfloor$ entries. These latin squares have at least $ 19 n^2/36 + O(n)$ transversal-
Externí odkaz:
http://arxiv.org/abs/2412.12466
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
A sequence covering array, denoted \textsf{SCA}$(N;t,v)$, is a set of $N$ permutations of $\{0, \dots, v-1 \}$ such that each sequence of $t$ distinct elements of $\{0, \dots, v-1\}$ reads left to right in at least one permutation. The minimum number
Externí odkaz:
http://arxiv.org/abs/2411.17145
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:
Baker, Sophie, Elliott, Gareth R., Wanless, Erica J., Webber, Grant B., Craig, Vincent S. J., Page, Alister J.
Over the last decade, experimental measurements of electrostatic screening lengths in concentrated electrolytes have exceeded theoretical predictions by orders of magnitude. This disagreement has led to a paradigm in which such screening lengths are
Externí odkaz:
http://arxiv.org/abs/2408.15685
Autor:
Devillers, Alice, Kamčev, Nina, McKay, Brendan, Catháin, Padraig Ó, Royle, Gordon, Van de Voorde, Geertrui, Wanless, Ian, Wood, David R.
There are finitely many graphs with diameter $2$ and girth 5. What if the girth 5 assumption is relaxed? Apart from stars, are there finitely many triangle-free graphs with diameter $2$ and no $K_{2,3}$ subgraph? This question is related to the exist
Externí odkaz:
http://arxiv.org/abs/2406.00246
A Latin square of order $n$ is an $n\times n$ matrix in which each row and column contains each of $n$ symbols exactly once. For $\epsilon>0$, we show that with high probability a uniformly random Latin square of order $n$ has no proper subsquare of
Externí odkaz:
http://arxiv.org/abs/2402.06205
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:
Pozsgay, Balázs, Wanless, Ian M.
Publikováno v:
Quantum 8, 1339 (2024)
Absolutely maximally entangled (AME) states of $k$ qudits (also known as perfect tensors) are quantum states that have maximal entanglement for all possible bipartitions of the sites/parties. We consider the problem of whether such states can be deco
Externí odkaz:
http://arxiv.org/abs/2308.07042
Autor:
Bodkin, Carly, Wanless, Ian M.
Publikováno v:
Fields Inst. Commun. 86, (2024), 1-23
A \emph{frequency square} is a matrix in which each row and column is a permutation of the same multiset of symbols. Two frequency squares $F_1$ and $F_2$ with symbol multisets $M_1$ and $M_2$ are \emph{orthogonal} if the multiset of pairs obtained b
Externí odkaz:
http://arxiv.org/abs/2212.01746