Improved and sharp bounds for illumination
We prove improved ordinary illumination bounds and exact ordinary and fractional values for several classes of convex bodies. Every full-dimensional complex zonotope in $\C^2$ has illumination number five, except complex affine images of the bidisc, whose number is seven. For complex $1$-symmetric non-polydiscs in $\C^3$, an explicit construction gives twelve illuminating directions. For real $1$-symmetric non-cubes in $\R^n$, connected domination in the cube graph gives the upper bound $2^{n-1}+\gamma_c(Q_{n-1})+n-1 =2^{n-1}(1+(1+o(1))/n)$; an explicit family has illumination number…
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