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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 6, Pages 187–210 (Mi izv672)  

This article is cited in 6 scientific papers (total in 6 papers)

On the theory of mainstay parallelohedra

S. S. Ryshkova, E. A. Bolshakovab

a Steklov Mathematical Institute, Russian Academy of Sciences
b M. V. Lomonosov Moscow State University

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 $(n'\leqslant n)$ mainstay parallelohedra situated in a special way. This paper contains a detailed proof of this theorem in a refined and definitive form.

DOI: https://doi.org/10.4213/im672

Full text: PDF file (1964 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2005, 69:6, 1257–1277

Bibliographic databases:

UDC: 511.9+514.174
MSC: 51M20, 51H20, 11H55, 11H31, 52C17, 52C07, 11H06
Received: 20.10.2004

Citation: S. S. Ryshkov, E. A. Bolshakova, “On the theory of mainstay parallelohedra”, Izv. RAN. Ser. Mat., 69:6 (2005), 187–210; Izv. Math., 69:6 (2005), 1257–1277

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. A. Bolshakova, “Nonprimitive $n$-dimensional parallelohedra of the first type: combinatorics and symbols”, Russian Math. Surveys, 61:3 (2006), 557–559  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. V. P. Grishukhin, “Minkowski sum of a parallelotope and a segment”, Sb. Math., 197:10 (2006), 1417–1433  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Dutour Sikirić M., Grishukhin V., “The decomposition of the hypermetric cone into $L$-domains”, European J. Combin., 30:4 (2009), 853–865  crossref  mathscinet  zmath  isi  elib  scopus
    4. V. P. Grishukhin, “The Voronoi polyhedra of the rooted lattice $E_6$ and of its dual lattice”, Discrete Math. Appl., 21:1 (2011), 91–108  mathnet  crossref  crossref  mathscinet  elib
    5. V. P. Grishukhin, “Parallelohedra defined by quadratic forms”, Proc. Steklov Inst. Math., 288 (2015), 81–93  mathnet  crossref  crossref  isi  elib
    6. Garber A., “On Pi-Surfaces of Four-Dimensional Parallelohedra”, Ann. Comb., 21:4 (2017), 551–572  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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