EXTREMAL FROBENIUS NUMBERS IN A CLASS OF SETS

For given A(k) = {a(1),...,a(k)},a(1)< ... < a(k) coprime the Frobeniu s number g(A(k)) is defined as the greatest integer g with no represen tation g = Sigma(i=1)(k) x(i)a(i), x(i) is an element of N-0. A class A(k) is given, such that (g) over bar* (k,y) := max {g(A(k))\A(k) is an element of A(k), a(k) less than or equal to y} has the same asympt otic behaviour as the general function (g) over bar(k,y) := max{g(A(k) )\a(k) less than or equal to y} for y --> infinity. Furthermore, (g) u nder bar(k,x) := min {g(A(k))\A(k) is an element of A(k)*, a(1) great er than or equal to x} is shown to have the same order of magnitude as the general function (g) under bar(k,x) := min {g(A(k))\a(1) greater than or equal to x} for x --> infinity.