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Let k be an infinite field and A a standard G-algebra. This means that there exists a positive integer n such that A = R/I where R is the polynomial ring R := k[Xv ..., Xn] and I is an homogeneous ideal of R. Thus the additive group of A has a direct sum decomposition A = ⊕ At where AiAj ⊆ Ai+j . Hence, for every t ≥ 0, At is a finite-dimensional vector space over k. The Hilbert Function of A is defined bydoi:10.1017/s0027763000005201 fatcat:q2sztx6kivghfmsrfq4axjburi