Subset ( a ) is obtained by fixing all indices m i to 1 , except for the last index, m n , which is incremented from 1 to g = 3 . Subset ( b ) is obtained by fixing m 1 = m 2 = 1 , and incrementing m 3 from 2 to g = 3 . Due to the constraint m i ≥ ≥ m i − − 1 on the indices in S ( n , g ) , the index m 4 must automatically take values in { 2 , 3 } . The construction of subsets ( c ) and ( d ) follows in the same manner.