Young symmetrizers and additive theory

For lambda partition of m and A finite nonempty subset of a field we define the set of lambda-restricted sums of m -tuples of elements of A , boolean AND m lambda A , and using Additive Number Theory results from [J.A. Dias da Silva and Y.O. Hamidoune ( 1990 ). A note on the minimal polynomial of the Kronecker sum of two linear operators. Linear Algebra Appl. , 141 , 283-287; J.A. Dias da Silva and Y.O. Hamidoune ( 1994 ). Cyclic spaces for Grassmann derivatives and additive theory. Bull. London Math. Soc. , 26 , 140-146] we obtain a lower bound for its cardinality. Next, using results and techniques from [J.A. Dias da Silva and Y.O. Hamidoune ( 1990 ). A note on the minimal polynomial of the Kronecker sum of two linear operators. Linear Algebra Appl. , 141 , 283-287; J.A. Dias da Silva and Y.O. Hamidoune ( 1994 ). Cyclic spaces for Grassmann derivatives and additive theory. Bull. London Math. Soc. , 26 , 140-146] we obtain lower bounds for the degrees of minimal polynomials of restrictions of derivations to ranges of Young symmetrizers and to the symmetry class of tensors V lambda , and we show that the lower bound for the cardinality of boolean AND m lambda A can also be obtained from these lower bounds.