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    Symmetric Difference-Free and Symmetric Difference-Closed Collections of Sets

    Access Status
    Fulltext not available
    Authors
    Gamble, Gregory
    Simpson, Jamie
    Date
    2013
    Type
    Journal Article
    
    Metadata
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    Citation
    Gamble, G. and Simpson, J. 2013. Symmetric Difference-Free and Symmetric Difference-Closed Collections of Sets. Graphs and Combinatorics. [In Press].
    Source Title
    Graphs and Combinatorics
    DOI
    10.1007/s00373-013-1388-7
    ISSN
    0911-0119
    URI
    http://hdl.handle.net/20.500.11937/3743
    Collection
    • Curtin Research Publications
    Abstract

    A collection of sets is symmetric-difference-free, respectively symmetric difference-closed, if the symmetric difference of any two sets in the collection lies outside, respectively inside, the collection. Recently Buck and Godbole (Size-maximal symmetric difference-free families of subsets of [n], Graphs Combin. (to appear), 2013) investigated such collections and showed, in particular, that the largest symmetric difference-free collection of subsets of an n-set has cardinality 2 n-1. We use group theory to obtain shorter proofs of their results.

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