Observe that for each permutation ϕ of the symmetric group S r , G → ( a 1 , . . . , a r ) ⇐⇒ G → ( a ϕ (1) , . . . , a ϕ ( r ) ). Therefore, we can assume that a 1 ≤ . . . ≤ a r . Note that if a 1 = 1, then F ( a 1 , . . . , a r ; q ) = F ( a 2 , . . . , a r ; q ). So, we will consider only Folkman numbers for which a i ≥ 2 , i = 1 , . . . , r .