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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 500, Pages 55–61
DOI: https://doi.org/10.31857/S2686954321050118
(Mi danma203)
 

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Self-affine tiling of polyhedra

V. Yu. Protasovab, T. I. Zaitsevacd

a University of L’Aquila, Aquila, Italy
b Lomonosov Moscow State University, Moscow, Russia
c Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia
d Laboratory "Multidimensional Approximation and Applications", Lomonosov Moscow State University, Moscow, Russia
References:
Abstract: We obtain a complete classification of polyhedral sets (unions of finitely many convex polyhedra) that admit self-affine tilings, i.e., partitions into parallel shifts of one set that is affinely similar to the initial one. In every dimension, there exist infinitely many nonequivalent polyhedral sets possessing this property. Under an additional assumption that the affine similarity is defined by an integer matrix and by integer shifts (“digits”) from different quotient classes with respect to this matrix, the only polyhedral set of this kind is a parallelepiped. Applications to multivariate wavelets and to Haar systems are discussed.
Keywords: tiling, self-affinity, tile, polyhedron, integer attractor, cone, Haar system.
Funding agency Grant number
Russian Foundation for Basic Research 19-04-01227
20-01-00469
Ministry of Education and Science of the Russian Federation 14.W03.31.0031
This work was supported by the Russian Foundation for Basic Research, project nos. 19-04-01227 and 20-01-00469. The second author’s research was supported by a grant from the Government of the Russian Federation for the state support of scientific research conducted under the direction of leading researchers, project no. 14.W03.31.0031.
Received: 15.06.2021
Revised: 15.06.2021
Accepted: 18.08.2021
English version:
Doklady Mathematics, 2021, Volume 104, Issue 2, Pages 267–272
DOI: https://doi.org/10.1134/S1064562421050112
Bibliographic databases:
Document Type: Article
UDC: 514.174.5, 519.148, 517.518.36, 517.965
Language: Russian
Citation: V. Yu. Protasov, T. I. Zaitseva, “Self-affine tiling of polyhedra”, Dokl. RAN. Math. Inf. Proc. Upr., 500 (2021), 55–61; Dokl. Math., 104:2 (2021), 267–272
Citation in format AMSBIB
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\by V.~Yu.~Protasov, T.~I.~Zaitseva
\paper Self-affine tiling of polyhedra
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2021
\vol 500
\pages 55--61
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\transl
\jour Dokl. Math.
\yr 2021
\vol 104
\issue 2
\pages 267--272
\crossref{https://doi.org/10.1134/S1064562421050112}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85124341772}
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  • This publication is cited in the following 1 articles:
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    Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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    References:21
     
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