Narodna in univerzitetna knjižnica, Ljubljana (NUK)
Naročanje gradiva za izposojo na dom
Naročanje gradiva za izposojo v čitalnice
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Urnik dostave gradiva z oznako DS v signaturi
  • Motion and distinguishing number two
    Conder, Marston D. E. ; Tucker, Thomas W.
    A group ▫$A$▫ acting faithfully on a finite set ▫$X$▫ is said to have distinguishing number two if there is a proper subset ▫$Y$▫ whose (setwise) stabilizer is trivial. The motion of ▫$A$▫ acting on ... ▫$X$▫ is defined as the largest integer ▫$k$▫ such that all non-trivial elements of ▫$A$▫ move at least ▫$k$▫ elements of ▫$X$▫. The Motion Lemma of Russell and Sundaram states that if the motion is at least ▫$2 \log_2 |A|$▫, then the action has distinguishing number two. When ▫$X$▫ is a vector space, group, or map, the Motion Lemma and elementary estimates of the motion together show that in all but finitely many cases, the action of Aut▫$(X)$▫ on ▫$X$▫ has distinguishing number two. A new lower bound for the motion of any transitive action gives similar results for transitive actions with restricted point-stabilizers. As an instance of what can happen with intransitive actions, it is shown that if ▫$X$▫ is a set of points on a closed surface of genus ▫$g$▫, and ▫$|X|$▫ is sufficiently large with respect to ▫$g$▫, then any action on ▫$X$▫ by a finite group of surface homeomorphisms has distinguishing number two.
    Vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 4, no. 1, 2011, str. 63-72)
    Vrsta gradiva - članek, sestavni del
    Leto - 2011
    Jezik - angleški
    COBISS.SI-ID - 16262489

    Povezava(-e):

    http://amc.imfm.si/index.php/amc/article/view/192
    Digitalna knjižnica Slovenije - dLib.si

vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 4, no. 1, 2011, str. 63-72)

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