Let or , where is a field of arbitrary characteristic and are indeterminates. In this paper we will show that there is an order preserving embedding from the poset of Hilbert functions of homogeneous ideals of to the poset of homogeneous ideals of . We also obtain related results for Betti numbers when the characteristic of is .
"Poset embeddings of Hilbert functions for two hypersurface rings." J. Commut. Algebra 12 (3) 371 - 389, Fall 2020. https://doi.org/10.1216/jca.2020.12.371