Structural Szemerédi-Trotter for Lattices and their Generalizations
DOI:
10.37236/12466
Publication Date:
2025-03-16T21:22:26Z
AUTHORS (3)
ABSTRACT
We completely characterize point-line configurations with $\Theta(n^{4/3})$ incidences when the point set is a section of integer lattice. This can be seen as main special case structural Szemerédi-Trotter problem. also derive partial characterization for several generalizations: (i) rule out concurrent lines Cartesian product an arithmetic progression and arbitrary set. (ii) study where one or both sets are generalized progression. Our proofs rely on deriving properties multiplicative energies.
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