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pro vyhledávání: '"Wanless, Ian"'
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:
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
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:
Drápal, Aleš, Wanless, Ian M.
Publikováno v:
Proc. Edinburgh Math. Soc. 66 (2023), 1085-1109
Let $\mathbb{F}$ be a finite field of odd order and $a,b\in\mathbb{F}\setminus\{0,1\}$ be such that $\chi(a) = \chi(b)$ and $\chi(1-a)=\chi(1-b)$, where $\chi$ is the extended quadratic character. Let $Q_{a,b}$ be the quasigroup upon $\mathbb{F}$ def
Externí odkaz:
http://arxiv.org/abs/2211.09472
We consider dual unitary operators and their multi-leg generalizations that have appeared at various places in the literature. These objects can be related to multi-party quantum states with special entanglement patterns: the sites are arranged in a
Externí odkaz:
http://arxiv.org/abs/2210.13017
Autor:
Gill, Michael J., Wanless, Ian M.
Publikováno v:
Des. Codes Cryptogr. 91 (2023), 1293-1313
A relation on a $k$-net$(n)$ (or, equivalently, a set of $k-2$ mutually orthogonal Latin squares of order $n$) is an $\mathbb{F}_{2}$ linear dependence within the incidence matrix of the net. Dukes and Howard (2014) showed that any 6-net(10) satisfie
Externí odkaz:
http://arxiv.org/abs/2204.10996