Octants are Cover-Decomposable into Many Coverings
  We prove that octants are cover-decomposable into multiple coverings, i.e., for any k there is an m(k) such that any m(k)-fold covering of any subset of the space with a finite number of translates of a given octant can be decomposed into k coverings. As a corollary, we obtain that any m(k)-fold covering of any subset of the plane with a finite number of homothetic copies of a given triangle can be decomposed into k coverings. Previously only some weaker bounds were known for related problems. 
Bal\'azs Keszegh and D\"om\"ot\"or P\'alv\"olgyi
math.CO cs.DM