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arXiv · 1610.02539

Additive Combinatorics Using Equivariant Cohomology

László M. Fehér·János Nagy
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Abstract

We introduce a geometric method to study additive combinatorial problems. Using equivariant cohomology we reprove the Dias da Silva-Hamidoune theorem. We improve a result of Sun on the linear extension of the Erd\H{o}s-Heilbronn conjecture. We generalize a theorem of G. K\'os (the Grashopper problem) which in some sense is a simultaneous generalization of the Erd\H{o}s-Heilbronn conjecture. We also prove a signed version of the Erd\H{o}s-Heilbronn conjecture and the Grashopper problem. Most identities used are based on calculating the projective degree of an algebraic variety in two different ways.

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László M. Fehér, János Nagy. 2016-10-08. Additive Combinatorics Using Equivariant Cohomology. https://arxiv.org/abs/1610.02539

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