Incongruent equipartitions of the plane into quadrangles of equal perimeters

Frettlöh D, Richter C (2021)
Journal of Combinatorial Theory, Series A 182: 105461.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Frettlöh, DirkUniBi; Richter, Christian
Abstract / Bemerkung
Motivated by a question of R. Nandakumar, we show that the Euclidean plane can be dissected into mutually incongruent convex quadrangles of the same area and the same perimeter. As a byproduct we obtain vertex-to-vertex dissections of the plane by mutually incongruent triangles of unit area that are arbitrarily close to the periodic vertex-to-vertex tiling by equilateral triangles. (C) 2021 Elsevier Inc. All rights reserved.
Stichworte
Equipartition; Fair partition; Tiling; Dissection; Equilateral triangle; Quadrangle
Erscheinungsjahr
2021
Zeitschriftentitel
Journal of Combinatorial Theory, Series A
Band
182
Art.-Nr.
105461
ISSN
0097-3165
eISSN
1096-0899
Page URI
https://pub.uni-bielefeld.de/record/2955347

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Frettlöh D, Richter C. Incongruent equipartitions of the plane into quadrangles of equal perimeters. Journal of Combinatorial Theory, Series A. 2021;182: 105461.
Frettlöh, D., & Richter, C. (2021). Incongruent equipartitions of the plane into quadrangles of equal perimeters. Journal of Combinatorial Theory, Series A, 182, 105461. https://doi.org/10.1016/j.jcta.2021.105461
Frettlöh, D., and Richter, C. (2021). Incongruent equipartitions of the plane into quadrangles of equal perimeters. Journal of Combinatorial Theory, Series A 182:105461.
Frettlöh, D., & Richter, C., 2021. Incongruent equipartitions of the plane into quadrangles of equal perimeters. Journal of Combinatorial Theory, Series A, 182: 105461.
D. Frettlöh and C. Richter, “Incongruent equipartitions of the plane into quadrangles of equal perimeters”, Journal of Combinatorial Theory, Series A, vol. 182, 2021, : 105461.
Frettlöh, D., Richter, C.: Incongruent equipartitions of the plane into quadrangles of equal perimeters. Journal of Combinatorial Theory, Series A. 182, : 105461 (2021).
Frettlöh, Dirk, and Richter, Christian. “Incongruent equipartitions of the plane into quadrangles of equal perimeters”. Journal of Combinatorial Theory, Series A 182 (2021): 105461.

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