Zoltán Lóránt Nagy: Maximizing the number of zero-sums

What is the maximum number of r-term subsequences admitting zero sum in n-element sequences of nonzero integers? We determine the maximum when r<4 or r>=n/2 and also in case when we drop the condition on the number of summands. We also explore some related problems. The main problem can be seen as a variant of the famous Erdős-Ginzburg-Ziv theorem (where the number of zero-sum sequences is minimized). We apply tools from algebra (vector space homomorphisms) and combinatorial arguments as well, such as a proof resembling to that of the Sperner theorem.
Joint work with Benjamin Móricz.

Link: https://us06web.zoom.us/j/87942357806?pwd=DObDjZ10qaD4guIVPhsO5QAJHqEVa2.1

Meeting ID: 879 4235 7806

Passcode: 279288