Illumination of several families of complex convex bodies
We determine ordinary and fractional illumination numbers for complex Hanner bodies and for bodies obtained as convex hulls of coordinate polydiscs indexed by the maximal independent sets of a graph. The formulas are sums over coordinate supports. For Hanner bodies we classify all equality cases in the ordinary and fractional dimension bounds, including the sharp ordinary bound for non-polydiscs. For graph bodies, fractional equality $2^n$ occurs exactly when the graph is a disjoint union of isolated vertices and edges; a vertex of degree at least two gives the strict bound $3\cdot2^{n-2}$.…
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