A note on the Manickam-Miklós-Singhi conjecture for vector spaces
@article{Ihringer2016ANO, title={A note on the Manickam-Mikl{\'o}s-Singhi conjecture for vector spaces}, author={Ferdinand Ihringer}, journal={Eur. J. Comb.}, year={2016}, volume={52}, pages={27-39} }
Let V be an n -dimensional vector space over a finite field with q elements. Define a real-valued weight function on the 1 -dimensional subspaces of V such that the sum of all weights is zero. Let the weight of a subspace S be the sum of the weights of the 1 -dimensional subspaces contained in S . In 1988 Manickam and Singhi conjectured that if n ? 4 k , then the number of k -dimensional subspaces with nonnegative weight is at least the number of k -dimensional subspaces on a fixed 1… CONTINUE READING
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