A note on equidistant permutation arrays

R. B. Eggleton; A. Hartman; D. A. Holton; Jennifer Seberry

doi:10.1007/BFb0062526

A note on equidistant permutation arrays

R. B. Eggleton
, A. Hartman
, D. A. Holton (Editor)
, Jennifer Seberry (Editor)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Two permutations on n elements are at (Hamming) distance μ if they disagree in exactly μ places. An equidistant permutation array is a collection of permutations on n elements, every pair of which is at distance μ. A permutation graph G(n,μ) is a graph with vertex set comprising all permutations on n elements, and edges between each pair of permutations at distance μ. These graphs enable the relevant permutation structure to be visualised; in particular, the cliques correspond to maximal equidistant permutation arrays. We obtain various structural theorems for these graphs, and conjecture several properties for their cliques.

Original language	English
Title of host publication	Proceedings of the Australian Combinatorics Conference
Subtitle of host publication	Combinatorial Mathematics
Editors	D.A. Holton, J. Seberry
Publisher	Springer
Pages	136-147
Number of pages	12
ISBN (Electronic)	978-3-540-35702-5
ISBN (Print)	978-3-540-08953-7
DOIs	https://doi.org/10.1007/BFb0062526
State	Published - 1978
Externally published	Yes

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10.1007/BFb0062526

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title = "A note on equidistant permutation arrays",

abstract = "Two permutations on n elements are at (Hamming) distance μ if they disagree in exactly μ places. An equidistant permutation array is a collection of permutations on n elements, every pair of which is at distance μ. A permutation graph G(n,μ) is a graph with vertex set comprising all permutations on n elements, and edges between each pair of permutations at distance μ. These graphs enable the relevant permutation structure to be visualised; in particular, the cliques correspond to maximal equidistant permutation arrays. We obtain various structural theorems for these graphs, and conjecture several properties for their cliques.",

author = "Eggleton, \{R. B.\} and A. Hartman and Holton, \{D. A.\} and Jennifer Seberry",

year = "1978",

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N2 - Two permutations on n elements are at (Hamming) distance μ if they disagree in exactly μ places. An equidistant permutation array is a collection of permutations on n elements, every pair of which is at distance μ. A permutation graph G(n,μ) is a graph with vertex set comprising all permutations on n elements, and edges between each pair of permutations at distance μ. These graphs enable the relevant permutation structure to be visualised; in particular, the cliques correspond to maximal equidistant permutation arrays. We obtain various structural theorems for these graphs, and conjecture several properties for their cliques.

AB - Two permutations on n elements are at (Hamming) distance μ if they disagree in exactly μ places. An equidistant permutation array is a collection of permutations on n elements, every pair of which is at distance μ. A permutation graph G(n,μ) is a graph with vertex set comprising all permutations on n elements, and edges between each pair of permutations at distance μ. These graphs enable the relevant permutation structure to be visualised; in particular, the cliques correspond to maximal equidistant permutation arrays. We obtain various structural theorems for these graphs, and conjecture several properties for their cliques.

U2 - 10.1007/BFb0062526

DO - 10.1007/BFb0062526

M3 - Conference contribution

SN - 978-3-540-08953-7

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BT - Proceedings of the Australian Combinatorics Conference

PB - Springer

ER -

A note on equidistant permutation arrays

Abstract

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