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Zapiski Nauchnykh Seminarov POMI, 2022, Volume 511, Pages 54–99
(Mi znsl7209)
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This article is cited in 1 scientific paper (total in 1 paper)
Combinatoric of the karyon tilings
V. G. Zhuravlev Vladimir State University
Abstract:
In this article, we study the combinatorial properties of the karyon tilings $\mathcal{T}$ of the torus $\mathbb{T}^d$ of an arbitrary dimension $d$. Our main results are the following statements: 1) the karyon corona $\mathbf{Cr}$ contains all types of polyhedral stars of the $\mathcal{T}$ tilings; 2) the number of all faces of dimension $a$ of the tiling $\mathcal{T}$ is equal to $md!/((d-a)!a!)$, where $m$ is the order of tilling.
Key words and phrases:
toric karyon tilings, classification, symmetries, combinatorics, local rules.
Received: 06.01.2021
Citation:
V. G. Zhuravlev, “Combinatoric of the karyon tilings”, Algebra and number theory. Part 5, Zap. Nauchn. Sem. POMI, 511, POMI, St. Petersburg, 2022, 54–99
Linking options:
https://www.mathnet.ru/eng/znsl7209 https://www.mathnet.ru/eng/znsl/v511/p54
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Abstract page: | 42 | Full-text PDF : | 23 | References: | 18 |
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