• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.15-21
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.735-740
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• 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.