The minimum length of a base for the symmetric group acting on partitions

C. Benbenishty, J.A. Cohen, Alice Niemeyer

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    A base for a permutation group, G, is a sequence of elements of its permutation domain whose stabiliser in G is trivial. Using purely elementary and constructive methods, we obtain bounds on the minimum length of a base for the action of the symmetric group on partitions of a set into blocks of equal size. This upper bound is a constant when the size of each block is at most equal to the number of blocks and logarithmic in the size of a block otherwise. These bounds are asymptotically best possible. (C) 2006 Elsevier Ltd. All rights reserved.
    Original languageEnglish
    Pages (from-to)1575-1581
    JournalEuropean Journal of Combinatorics
    Volume28
    Issue number6
    DOIs
    Publication statusPublished - 2007

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