Geodesic
Topological methods in zero-sum Ramsey theory
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e192

Voir la notice de l'article provenant de la source Cambridge University Press

A landmark result of Erdős, Ginzburg, and Ziv (EGZ) states that any sequence of $2n-1$ elements in ${\mathbb {Z}}/n$ contains a zero-sum subsequence of length n. While algebraic techniques have predominated in deriving many deep generalizations of this theorem over the past sixty years, here we introduce topological approaches to zero-sum problems which have proven fruitful in other combinatorial contexts. Our main result is a topological criterion for determining when any ${\mathbb {Z}}/n$-coloring of an n-uniform hypergraph contains a zero-sum hyperedge. In addition to applications for Kneser hypergraphs, for complete hypergraphs our methods recover Olson’s generalization of the EGZ theorem for arbitrary finite groups. Furthermore, we give a fractional generalization of the EGZ theorem with applications to balanced set families and provide a constrained EGZ theorem which imposes combinatorial restrictions on zero-sum sequences in the original result. 
Frick, Florian; Duke, Jacob Lehmann; McNamara, Meenakshi; Park-Kaufmann, Hannah; Raanes, Steven; Simon, Steven; Thornburgh, Darrion; Wellner, Zoe. Topological methods in zero-sum Ramsey theory. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e192. doi: 10.1017/fms.2025.10125
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     title = {Topological methods in zero-sum {Ramsey} theory},
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