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Optimally small sumsets in groups III. The generalized increasingly small sumsets property and the $\nu^{(k)}_G$} functions
In this third part of our work, we go back to the study of the $\nu^{(k)}_G$ functions (introduced in the first one), which count the minimal cardinality of a sumset containing an element with a single representation. An upper bound for these functions is obtained in the case $k=2$ using …