The Hilbert Function of a Level Algebra

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On higher Hessians and the Lefschetz properties (2015, background): “i → Ad ≃ Kis non-degenerate for every i = 0,...,[d 2]. The algebra A is said to be standard if A ≃ K[x0,...,x N] I , as graded algebras, with I ⊂ K[x 0,...,xN] a homogeneous ideal. Proposition 1.14. ([GHMS], [MW, Proposition 2.1]) Let A be a graded Artinian K-algebra. Then A satisﬁes the Poincar´e D”
On the shape of a pure O-sequence (2010, methodology): “el algebras, which then followed mostly independent paths from that of pure order ideals, also originated with Stanley’s work [64] (along with [65]). Among the several sources, we refer to the memoir [24] and to the works [75, 79] and their bibliographies for some of the most recent developments of ”
Lefschetz elements of Artinian Gorenstein algebras and Hessians of homogeneous polynomials (2009, background): “The Hilbert function of $A$ is Hilb$(A)=(1,3,3,1)$ for all $s\in k$ .”