VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • On the intersection density of the symmetric group acting on uniform subsets of small size
    Behajaina, Angelot ; Maleki, Roghayeh ; Razafimahatratra, Andriaherimanana Sarobidy
    Given a finite transitive group ▫$G\leq \sym(\Omega)$▫, a subset ▫$\mathcal{F}$▫ of ▫$G$▫ is \emph{intersecting} if any two elements of ▫$\mathcal{F}$▫ agree on some elements of ▫$\Omega$▫. The ... \emph{intersection density} of ▫$G$▫, denoted by ▫$\rho(G)$▫, is the maximum of the rational number ▫$|\mathcal{F}|\left(\frac{|G|}{|\Omega|}\right)^{-1}$▫ when ▫$\mathcal{F}$▫ runs through all intersecting sets in ▫$G$▫. In this paper, we prove that if ▫$G$▫ is the group ▫$\sym(n)$▫ or ▫$\alt(n)$▫ acting on the ▫$k$▫-subsets of ▫$\{1,2,3\ldots,n\}$▫, for ▫$k\in \{3,4,5\}$▫, then ▫$\rho(G)=1$▫. Our proof relies on the representation theory of the symmetric group and the ratio bound.
    Vir: Linear algebra and its applications. - ISSN 0024-3795 (Vol. 664, May 2023, str. 61-103)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2023
    Jezik - angleški
    COBISS.SI-ID - 140581635

    Povezava(-e):

    https://www.sciencedirect.com/science/article/pii/S0024379523000101
    https://doi.org/10.1016/j.laa.2023.01.010
    DOI

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