Abstract:
In 1998 the first author announced a theorem stating that every primitive n-dimensional parallelohedron can be represented, up to an affine transformation, as a weighted Minkowski sum of parallelohedra belonging to a certain finite set of n′-dimensional (n′⩽n) mainstay parallelohedra situated in a special way. This paper contains a detailed proof of this theorem in a refined and definitive form.
\Bibitem{RysBol05}
\by S.~S.~Ryshkov, E.~A.~Bolshakova
\paper On the theory of mainstay parallelohedra
\jour Izv. Math.
\yr 2005
\vol 69
\issue 6
\pages 1257--1277
\mathnet{http://mi.mathnet.ru/eng/im672}
\crossref{https://doi.org/10.1070/IM2005v069n06ABEH002298}
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Linking options:
https://www.mathnet.ru/eng/im672
https://doi.org/10.1070/IM2005v069n06ABEH002298
https://www.mathnet.ru/eng/im/v69/i6/p187
This publication is cited in the following 7 articles:
V. P. Grishukhin, “Layer Superposition of the Root Lattice An”, Math. Notes, 109:2 (2021), 218–230
Garber A., “On Pi-Surfaces of Four-Dimensional Parallelohedra”, Ann. Comb., 21:4 (2017), 551–572
V. P. Grishukhin, “Parallelohedra defined by quadratic forms”, Proc. Steklov Inst. Math., 288 (2015), 81–93
V. P. Grishukhin, “The Voronoi polyhedra of the rooted lattice E6 and of its dual lattice”, Discrete Math. Appl., 21:1 (2011), 91–108
Dutour Sikirić M., Grishukhin V., “The decomposition of the hypermetric cone into L-domains”, European J. Combin., 30:4 (2009), 853–865
E. A. Bolshakova, “Nonprimitive n-dimensional parallelohedra of the first type: combinatorics and symbols”, Russian Math. Surveys, 61:3 (2006), 557–559
V. P. Grishukhin, “Minkowski sum of a parallelotope and a segment”, Sb. Math., 197:10 (2006), 1417–1433
Citation in format AMSBIB
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