Additive Combinatorics Using Equivariant Cohomology

Fehér, László and Nagy, János (2023) Additive Combinatorics Using Equivariant Cohomology. ISRAEL JOURNAL OF MATHEMATICS. ISSN 0021-2172

Preview

Text 1610.02539v3.pdf Download (364kB) | Preview

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 Erdős-Heilbronn conjecture. We generalize a theorem of G. Kós (the Grashopper problem) which in some sense is a simultaneous generalization of the Erdős-Heilbronn conjecture. We also prove a signed version of the Erdős-Heilbronn conjecture and the Grashopper problem. Most identities used are based on calculating the projective degree of an algebraic variety in two different ways.

Actions (login required)

Edit Item