On combinatorial problem concerning partitions of a box into boxes
Abstract
We consider partitions of n-dimensional boxes in Rn, n>1, into a finite number of boxes with pairwise disjoint interiors. We study sets X ⊂eq (0,∞) with the Property (Wn): for every n-dimensional box P and every partition of P, if each constituent box has one side with the length belonging to X, then the length of one side of P belongs to X. We prove that the set X ⊂eq (0,∞) has Property (Wn) if and only if X is closed with respect to the operations: x+y and x+y+z-2min(x,y,z).
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.