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 proceedingConference contributionpeer-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 languageEnglish
Title of host publicationProceedings of the Australian Combinatorics Conference
Subtitle of host publicationCombinatorial Mathematics
EditorsD.A. Holton, J. Seberry
PublisherSpringer
Pages136-147
Number of pages12
ISBN (Electronic)978-3-540-35702-5
ISBN (Print)978-3-540-08953-7
DOIs
StatePublished - 1978
Externally publishedYes

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