Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4653186 | European Journal of Combinatorics | 2017 | 10 Pages |
Abstract
In this paper, we use methods from spectral graph theory to obtain some results on the sum-product problem over finite valuation rings R of order qr which generalize recent results given by Hegyvári and Hennecart (2013). More precisely, we prove that, for related pairs of two-variable functions f(x,y) and g(x,y), if A and B are two sets in Râ with |A|=|B|=qα, then max{|f(A,B)|,|g(A,B)|}â«|A|1+Î(α), for some Î(α)>0.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Le Quang Ham, Pham Van Thang, Le Anh Vinh,