On sets and configurations

Malabika Pramanik
When does a given set contain a copy of your favourite pattern (for example, specially arranged points on a line or a spiral, or the vertices of a polyhedron) Does the answer depend on how thin the set is in some quantifiable sense Problems involving identification of prescribed configurations under varying interpretations of size have been vigorously pursued both in the discrete and continuous setting, often with spectacular results that run contrary to intuition. Yet...
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