Polytopes of minimal null designs
Commun. Korean Math. Soc. 2002 Vol. 17, No. 1, 143-153
Printed March 1, 2002
Soojin Cho
Sejong University
Abstract : Null designs form a vector space and there are only finite number of minimal null designs(up to scalar multiple), hence it is natural to look at the convex polytopes of minimal null designs. For example, when $t=0,\, k=1$, the convex polytope of minimal null designs is the polytope of roots of type $A_n$. In this article, we look at the convex polytopes of minimal null designs and find many general properties on the vertices, edges, dimension, and some structural properties that might help to understand the structure of polytopes for big $n, t$ through the structure of smaller $n, t$.
Keywords : null designs, minimal null designs, polytopes of null designs
MSC numbers : 52B05, 05B99, 05D99, 06A07
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