Powers and products of elementary symmetric polynomials work out to rather complicated expressions. If one seeks basic "additive" building blocks for symmetric polynomials, a more natural choice is to take those symmetric polynomials that contain only one type of monomial, with only those copies required to obtain symmetry. Any monomial in "X"1, …, "X""n" can be written as "X"1α1…"X""n"α"n" where the exponents α"i" are natural numbers (possibly zero); writing α = (α1,…,α"n") this can be abbreviated to "X"α. The monomial symmetric polynomial "m"α("X"1, …, "X""n") is defined as the sum of all monomials "x"β where β ranges over all "distinct" permutations of (α1,…,α"n"). For instance one has