{"id":"hexagon/2611.00011","pdf":"https://hexagonmath.org/pdf/2611.00011v1","url":"https://hexagonmath.org/abs/2611.00011v1","tags":["msc:52A20","convex geometry"],"score":0,"title":"Improved and sharp bounds for illumination","domain":"math.MG","origin":"ai-generated","source":"hexagon","authors":["אלון שכטר"],"reviews":0,"subject":"math.MG","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}