Dot-Product Sets and Simplices Over Finite Rings
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DOI: 10.1007/s00041-022-09933-7
Abstract: In this paper, we study dot-product sets and k -simplices in $$\mathbb {Z}_n^d$$ Z n d for odd n , where $$\mathbb {Z}_n$$ Z n is the ring of residues modulo n . We show… read more here.
Keywords: dot product; product; finite rings; sets simplices ... See more keywords
ON ITERATED PRODUCT SETS WITH SHIFTS
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DOI: 10.1112/s0025579319000081
Abstract: We prove that, for any finite set $A \subset \mathbb Q$ with $|AA| \leq K|A|$ and any positive integer $k$, the $k$-fold product set of the shift $A+1$ satisfies the bound $$| \{(a_1+1)(a_2+1) \cdots (a_k+1)… read more here.
Keywords: product; sets shifts; product sets; iterated product ... See more keywords