Incongruent equipartitions of the plane

Frettlöh D, Richter C (2020)
EUROPEAN JOURNAL OF COMBINATORICS 87: 103129.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Autor*in
Frettlöh, DirkUniBi; Richter, Christian
Abstract / Bemerkung
R. Nandakumar asked whether there is a tiling of the plane by pairwise incongruent triangles of equal area and equal perimeter. Recently a negative answer was given by Kupayskii, Pach and Tardos. Still one may ask for weaker versions of the problem, or for the analogue of this problem for quadrangles, pentagons, or hexagons. Several answers were given by the first author in a previous paper. Here we solve three further cases. In particular, our main result shows that there are vertex-to-vertex tilings by pairwise incongruent triangles of unit area and bounded perimeter. (C) 2020 Elsevier Ltd. All rights reserved.
Erscheinungsjahr
2020
Zeitschriftentitel
EUROPEAN JOURNAL OF COMBINATORICS
Band
87
Art.-Nr.
103129
ISSN
0195-6698
eISSN
1095-9971
Page URI
https://pub.uni-bielefeld.de/record/2943572

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Frettlöh D, Richter C. Incongruent equipartitions of the plane. EUROPEAN JOURNAL OF COMBINATORICS. 2020;87: 103129.
Frettlöh, D., & Richter, C. (2020). Incongruent equipartitions of the plane. EUROPEAN JOURNAL OF COMBINATORICS, 87, 103129. doi:10.1016/j.ejc.2020.103129
Frettlöh, D., and Richter, C. (2020). Incongruent equipartitions of the plane. EUROPEAN JOURNAL OF COMBINATORICS 87:103129.
Frettlöh, D., & Richter, C., 2020. Incongruent equipartitions of the plane. EUROPEAN JOURNAL OF COMBINATORICS, 87: 103129.
D. Frettlöh and C. Richter, “Incongruent equipartitions of the plane”, EUROPEAN JOURNAL OF COMBINATORICS, vol. 87, 2020, : 103129.
Frettlöh, D., Richter, C.: Incongruent equipartitions of the plane. EUROPEAN JOURNAL OF COMBINATORICS. 87, : 103129 (2020).
Frettlöh, Dirk, and Richter, Christian. “Incongruent equipartitions of the plane”. EUROPEAN JOURNAL OF COMBINATORICS 87 (2020): 103129.