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Incidences and tilings
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We show that various classical theorems of real/complex linear incidence geometry, such as the theorems of Pappus, Desargues, M\"obius, and so on, can be interpreted as special cases of a single "master theorem" that involves an arbitrary tiling of a closed oriented surface by quadrilateral tiles. This yields a general mechanism for producing new incidence theorems and generalizing the known ones.
Forward citations
Cited by 3 Pith papers
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Tropical linear series and matroids
Tropical linear series on metric graphs are locally Bergman fans of matroids, yielding an exact condition for canonical tropicalizations to fill the realizable locus.
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Octagon and tropical octagon yield braid invariants
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