On combinatorial problem concerning partitions of a box into boxes

Details On combinatorial problem concerning partitions of a box into boxes On combinatorial problem concerning partitions of a box into boxes

2006-11-26

arxiv.org/abs/math/0611798v2

Journal of Natural Geometry 8 (1995), no. 2, pp. 129-132

Mathematics

Metric Geometry

3 pages, LaTeX2e, added the address http://www.cyf-kr.edu.pl/~rttyszka/jnatgeom1994.doc to item 4 of the References

Scientific paper

We consider partitions of n-dimensional boxes in R^n, n>1, into a finite number of boxes with pairwise disjoint interiors. We study sets X \subseteq (0,\infty) with the Property (W_n): 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 \subseteq (0,\infty) has Property (W_n) if and only if X is closed with respect to the operations: x+y and x+y+z-2min(x,y,z).

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