TY - JOUR
T1 - An upper bound for a valence of a face in a parallelohedral tiling
AU - Magazinov, Alexander
PY - 2013/10
Y1 - 2013/10
N2 - Consider a face-to-face parallelohedral tiling of Rd and a (d - k) -dimensional face F of the tiling. We prove that the valence of F (i.e.the number of tiles containing F as a face) is not greater than 2k. If the tiling is affinely equivalent to a Voronoi tiling for some lattice (the so called Voronoi case), this gives a well-known upper bound for the number of vertices of a Delaunay k-cell. Yet we emphasize that such an affine equivalence is not assumed in the proof.
AB - Consider a face-to-face parallelohedral tiling of Rd and a (d - k) -dimensional face F of the tiling. We prove that the valence of F (i.e.the number of tiles containing F as a face) is not greater than 2k. If the tiling is affinely equivalent to a Voronoi tiling for some lattice (the so called Voronoi case), this gives a well-known upper bound for the number of vertices of a Delaunay k-cell. Yet we emphasize that such an affine equivalence is not assumed in the proof.
UR - http://www.scopus.com/inward/record.url?scp=84876357937&partnerID=8YFLogxK
U2 - 10.1016/j.ejc.2013.02.004
DO - 10.1016/j.ejc.2013.02.004
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AN - SCOPUS:84876357937
SN - 0195-6698
VL - 34
SP - 1108
EP - 1113
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
IS - 7
ER -