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math.CO2024
Reptile trapezoids
Jin Heo
A geometric figure is a reptile if it can be dissected into at least two similar copies congruent to each other. We prove that if a trapezoid is a reptile and not a parallelogram,…
math.FA2024
Solutions to the discrete Pompeiu problem and to the finite Steinhaus tiling problem
Gergely Kiss, Miklós Laczkovich
Let be a nonempty finite subset of the Euclidean space . We prove that if a function is such that the sum of o…