Zobrazeno 1 - 10
of 112
pro vyhledávání: '"Frettlöh, Dirk"'
Autor:
Frettlöh, Dirk
A vertex colouring of some graph is called perfect if each vertex of colour $i$ has the same number $a_{ij}$ of neighbours of colour $j$. Here we determine all perfect colourings of the edge graphs of the hypercube in dimensions 4 and 5 by two and th
Externí odkaz:
http://arxiv.org/abs/2402.18457
In this work, we consider a class of substitutions on infinite alphabets and show that they exhibit a growth behaviour which is impossible for substitutions on finite alphabets. While for both settings the leading term of the tile counting function i
Externí odkaz:
http://arxiv.org/abs/2211.02548
Publikováno v:
Discrete Analysis 2024:11, 24 pp
For any $\lambda>2$, we construct a substitution on an infinite alphabet which gives rise to a substitution tiling with inflation factor $\lambda$. In particular, we obtain the first class of examples of substitutive systems with transcendental infla
Externí odkaz:
http://arxiv.org/abs/2208.01327
Publikováno v:
In Indagationes Mathematicae September 2024 35(5):890-913
Autor:
Frettlöh, Dirk, Richter, Christian
Motivated by a question of R.\ Nandakumar, we show that the Euclidean plane can be dissected into mutually incongruent convex pentagons of the same area and the same perimeter.
Comment: 6 pages, 2 figures
Comment: 6 pages, 2 figures
Externí odkaz:
http://arxiv.org/abs/2202.01674
Two Delone sets are bounded distance equivalent to each other if there is a bijection between them such that the distance of corresponding points is uniformly bounded. Bounded distance equivalence is an equivalence relation. We show that the hull of
Externí odkaz:
http://arxiv.org/abs/2101.02514
Autor:
Frettlöh, Dirk, Richter, Christian
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 m
Externí odkaz:
http://arxiv.org/abs/2004.01034
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An irregular vertex in a tiling by polygons is a vertex of one tile and belongs to the interior of an edge of another tile. In this paper we show that for any integer $k\geq 3$, there exists a normal tiling of the Euclidean plane by convex hexagons o
Externí odkaz:
http://arxiv.org/abs/1911.12752
In the study of aperiodic order and mathematical models of quasicrystals, questions regarding equivalence relations on Delone sets naturally arise. This work is dedicated to the bounded displacement (BD) equivalence relation, and especially to result
Externí odkaz:
http://arxiv.org/abs/1907.01597