Expansion for the product of matrices in groups

2018/03/09 by Doowon Koh, Thang Pham, Koh, Doowon +5
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1803.03351

v2: we have added some improvements

arxiv created 2018/03/28 · arxiv updated 2018/03/29

Abstract

In this paper, we give strong lower bounds on the size of the sets of products of matrices in some certain groups. More precisely, we prove an analogue of a result due to Chapman and Iosevich for matrices in SL₂(\mathbbF_p) with restricted entries on a small set. We also provide extensions of some recent results on expansion for cubes in Heisenberg group due to Hegyvári and Hennecart.

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