Cauchy-Davenport Theorem for linear maps: Simplification and Extension
  We give a new proof of the Cauchy-Davenport Theorem for linear maps given by Herdade et al., (2015). This theorem gives a lower bound on the size of the image of a linear map on a grid. Our proof is purely combinatorial and offers a partial insight into the range of parameters not handled previously. 
John Kim, Aditya Potukuchi
math.CO