2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118125The well-known "splitting necklace theorem" of Noga Alon says that each "necklace" having beads of n different colors can be fairly divided between k "thieves" by at most n(k-1) cuts. We demonstrate that Alon's result is a special case of a multidimensional, consensus division theorem for n continuous probability measures on a d-cube [0,1]^d. The dissection is performed by m_1+...+ m_d=n(k-1) hyperplanes parallel to the sides of [0,1]^d dividing the cube into m_1 x m_2 x ... x m_d elementary parallelepipeds where the integers m_i are prescribed in advance.CombinatoricsAlgebraic Topology05C10; 51M16, 52A40, 52B22, 55N91text