Arithmetic properties of exceptional lattice paths
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Arithmetic properties of exceptional lattice paths
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| Creator |
Rump, W.
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| Description |
For a fixed real number ρ > 0, let L be an affine line of slope ρ ⁻¹ in R ² . We show that the closest approximation of L by a path P in Z ² is unique, except in one case, up to integral translation. We study this exceptional case. For irrational ρ, the projection of P to L yields two quasicrystallographic tilings in the sense of Lunnon and Pleasants [5]. If ρ satisfies an equation x ² = mx + 1 with m ∈ Z, both quasicrystals are mapped to each other by a substitution rule. For rational ρ, we characterize the periodic parts of P by geometric and arithmetic properties, and exhibit a relationship to the hereditary algebras Hρ(K) over a field K introduced in a recent proof of a conjecture of Ro˘ıter. |
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| Date |
2019-06-20T03:11:02Z
2019-06-20T03:11:02Z 2006 |
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| Type |
Article
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| Identifier |
Arithmetic properties of exceptional lattice paths / W. Rump // Algebra and Discrete Mathematics. — 2006. — Vol. 5, № 3. — С. 101–118. — Бібліогр.: 16 назв. — англ.
1726-3255 2000 Mathematics Subject Classification: 05B30, 11B50; 52C35, 11A0 http://dspace.nbuv.gov.ua/handle/123456789/157386 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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