On the Independence Numbers of the Van der Waerden and cyclic Van der Waerden Hypergraphs W(k,t) and W_C(k,t) When t and k Are Powers of the Same Prime

摘要

For integers 1 ≤m≤n and a prime p (we require 2≤m when p = 2), a subset I(p~n,p~m) ? {0,… p~n-1}is described which contains no p~m-term cyclic arithmetic progression modulo p~n, and which is maximal among subsets of {0,…p~n-1} with that property.