30 citations · 62 across the 11 of their papers we have counts for
13 papers
Perfect colourings of simplices and hypercubes in dimension four and five with few colours
Dirk Frettlöh
A vertex colouring of some graph is called perfect if each vertex of colour has the same number of neighbours of colour . Here we determine all perfect colourings o…
Substitution tilings with transcendental inflation factor
Dirk Frettlöh, Alexey Garber, Neil Mañibo
For any , we construct a substitution on an infinite alphabet which gives rise to a substitution tiling with inflation factor . In particular, we obtain the first class of…
Number of bounded distance equivalence classes in hulls of repetitive Delone sets
Dirk Frettlöh, Alexey Garber, Lorenzo Sadun
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 dist…
Perfect colourings of regular graphs
Joseph R. C. Damasco, Dirk Frettlöh
A vertex colouring of some graph is called perfect if each vertex of colour has exactly neighbours of colour . Being perfect imposes several restrictions on the col…
Noncongruent equidissections of the plane
Dirk Frettlöh
Nandakumar asked whether there is a tiling of the plane by pairwise non-congruent triangles of equal area and equal perimeter. Here a weaker result is obtained: there is a tiling o…
Highly symmetric fundamental domains for lattices in R^2 and R^3
Joseph Ray Clarence G. Damasco, Dirk Frettlöh, Manuel Joseph C. Loquias
It is shown that most lattices in and possess a fundamental domain for the action of on , respectively , havin…