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  • A partial generalization of the Livingstone-Wagner Theorem
    Nakashima, Yasuhiro
    For a transitive permutation group ▫$G$▫ on a finite set ▫$\Omega$▫, the Livingstone-Wagner Theorem states that if ▫$G$▫ is ▫$k$▫-homogeneous and ▫$2 \le k \le \frac{\vert \Omega \vert}{2}$▫, then ... ▫$G$▫ is ▫$(k - 1)$▫-transitive. We conjecture that the number of ▫$G$▫-orbits on ▫$k$▫-subsets of ▫$\Omega$▫ is greater than or equal to the number of ▫$G$▫-orbits on ordered ▫$(k - 1)$▫-tuples of ▫$\Omega$▫, if ▫$\vert \Omega \vert$▫ is sufficiently large. For the simplest case ▫$k = 3$▫, we verify this conjecture by establishing a result on edge-colorings of complete digraphs.
    Vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 2, no. 2, 2009, str. 207-215)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2009
    Jezik - angleški
    COBISS.SI-ID - 15498585

    Povezava(-e):

    http://amc.imfm.si/index.php/amc/article/viewFile/92/78
    Digitalna knjižnica Slovenije - dLib.si

vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 2, no. 2, 2009, str. 207-215)

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