• Title/Summary/Keyword: dual polar spaces

Search Result 2, Processing Time 0.016 seconds

A NOTE ON NULL DESIGNS OF DUAL POLAR SPACES

  • CHO, SOO-JIN
    • Communications of the Korean Mathematical Society
    • /
    • v.20 no.1
    • /
    • pp.15-21
    • /
    • 2005
  • Null designs on the poset of dual polar spaces are considered. A poset of dual polar spaces is the set of isotropic subspaces of a finite vector space equipped with a nondegenerate bilinear form, ordered by inclusion. We show that the minimum number of isotropic subspaces to construct a nonzero null t-design is ${\prod}^{t}_{i=0}(1+q^{i})$ for the types $B_N,\;D_N$, whereas for the case of type $C_N$, more isotropic subspaces are needed.

VOLUME PRODUCT FOR PEDAL BODIES

  • Chai, Y.D.;Kim, Yong-Il;Lee, Doo-Hann
    • Bulletin of the Korean Mathematical Society
    • /
    • v.38 no.4
    • /
    • pp.735-740
    • /
    • 2001
  • Let K be a convex body of constant relative breadth and let $K^*$ be its polar dual with respect to the Euclidean unit circle. In this paper we obtain the lower bound for the volume of the pedal body $PK^*P $K^{*}$ of K^*.$ Using this, we also obtain the lower bound for the volume product V$(PK^*)$V(PK) for planar bodies.s.

  • PDF