Ian M. Wanless

activity

20092026

most citedAutoparatopisms of Quasigroups and Latin Squares

12 citations · 51 across the 27 of their papers we have counts for

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Showing 2024Show all

6 papers · 1 filter

math.CO2024

Latin Squares whose transversals share many entries

Afsane Ghafari, Ian M. Wanless

We prove that, for all even $n \geq 10$ , there exists a latin square of order $n$ with at least one transversal, yet all transversals coincide on $⌊ n /6 ⌋$ entri…

math.CO2024

Commuting Pairs in Quasigroups

Jack Allsop, Ian M. Wanless

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 t…

math.CO2024

Excess Coverage Arrays and Levenshtein's Conjecture

Amber E. Gentle, Daniel Horsley, Ian M. Wanless

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\…

math.CO2024

Subsquares in random Latin rectangles

Jack Allsop, Ian M. Wanless

Suppose that $k$ is a function of $n$ and $n \to \infty$ . We show that with probability $1 - O (1/ n)$ , a uniformly random $k \times n$ Latin rectangle contains no proper Latin subsquare…

math.CO2024

Triangle-free graphs with diameter 2

Alice Devillers, Nina Kamčev, Brendan McKay +5

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 diamete…

math.CO2024★ 1 cited

Canonical labelling of Latin squares in average-case polynomial time

Michael J. Gill, Adam Mammoliti, Ian M. Wanless

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 $ε > 0$ , we show that with high probability a uniform…