TY - JOUR
T1 - Voronoi’s Conjecture for extensions of Voronoi parallelohedra
AU - Magazinov, Alexander
N1 - Publisher Copyright:
© 2015, Mathematical Sciences Publishers. All rights reserved.
PY - 2015
Y1 - 2015
N2 - In 1908 Voronoi conjectured that every parallelohedron is a a Voronoi parallelohedron for some Euclidean metric in Ed. Although the conjecture is still neither proved, nor disproved, there are several positive results for some special classes of parallelohedra. In this paper we extend the list of such classes by one new case. Let I be a segment in the d-dimensional Euclidean space Ed. Let P and P + I be parallelohedra in Ed, where the plus sign denotes the Minkowski sum. We prove that, if Voronoi’s Conjecture holds for P, then Voronoi’s Conjecture holds for P + I as well.
AB - In 1908 Voronoi conjectured that every parallelohedron is a a Voronoi parallelohedron for some Euclidean metric in Ed. Although the conjecture is still neither proved, nor disproved, there are several positive results for some special classes of parallelohedra. In this paper we extend the list of such classes by one new case. Let I be a segment in the d-dimensional Euclidean space Ed. Let P and P + I be parallelohedra in Ed, where the plus sign denotes the Minkowski sum. We prove that, if Voronoi’s Conjecture holds for P, then Voronoi’s Conjecture holds for P + I as well.
KW - Voronoi’s Conjecture
KW - free segment
KW - parallelohedron
KW - reducible parallelohedron
KW - tiling
UR - http://www.scopus.com/inward/record.url?scp=85052712887&partnerID=8YFLogxK
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85052712887
SN - 2220-5438
VL - 5
SP - 86
EP - 131
JO - Moscow Journal of Combinatorics and Number Theory
JF - Moscow Journal of Combinatorics and Number Theory
IS - 3
ER -