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math.CO2026
The sad life of lattice triangles
Christian Aebi, Grant Cairns
This paper treats triangles in the plane whose vertices lie on the integer lattice, i.e., the vertices have integer coordinates. It shows that apart from trivial examples, the circ…
math.CO2024
Equable Parallelograms on the Eisenstein Lattice
Christian Aebi, Grant Cairns
This paper studies equable parallelograms whose vertices lie on the Eisenstein lattice. Using Rosenberger's Theorem on generalised Markov equations, we show that the set of these p…
math.CO2023
Less than Equable Triangles on the Eisenstein lattice
Christian Aebi, Grant Cairns
We classify perimeter dominant triangles whose side lengths are in and whose area is in . There is one exceptional example, which is equi…