S. Blackburn

activity

20082023

most citedNon-overlapping codes

40 citations · 178 across the 25 of their papers we have counts for

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13 papers · 1 filter

math.CO2023

Permutations that separate close elements, and rectangle packings in the torus

Simon R. Blackburn, Tuvi Etzion

Let $n$ , $s$ and $k$ be positive integers. For distinct $i, j \in Z_{n}$ , define $∣∣ i, j ∣ ∣_{n}$ to be the distance between $i$ and $j$ when the elements of $Z_{n}$ are writ…

math.CO2022

Permutations that separate close elements

Simon R. Blackburn

Let $n$ be a fixed integer with $n \geq 2$ . For $i, j \in Z_{n}$ , define $∣∣ i, j ∣ ∣_{n}$ to be the distance between $i$ and $j$ when the elements of $Z_{n}$ are written in a…

math.CO2021

The enumeration of finite rings

Simon R. Blackburn, K. Robin McLean

Let $p$ be a fixed prime. We show that the number of isomorphism classes of finite rings of order $p^{n}$ is $p^{α}$ , where $α = \frac{4}{27} n^{3} + O (n^{5/2})$ . This result was stated (with…

math.CO2020

Block-avoiding point sequencings

Simon R. Blackburn, Tuvi Etzion

Let $n$ and $ℓ$ be positive integers. Recent papers by Kreher, Stinson and Veitch have explored variants of the problem of ordering the points in a triple system (such as a Stei…

math.CO2018

Inglenook Shunting Puzzles

Simon R. Blackburn

An inglenook puzzle is a classic shunting (switching) puzzle often found on model railway layouts. A collection of wagons sits in a fan of sidings with a limited length headshunt (…

math.CO2017

The minimum Manhattan distance and minimum jump of permutations

Simon R. Blackburn, Cheyne Homberger, Peter Winkler

Let $π$ be a permutation of ${1, 2, \dots, n}$ . If we identify a permutation with its graph, namely the set of $n$ dots at positions $(i, π (i))$ , it is natural to consider the minim…