In this paper, we prove some special cases of the Eisenbud–Green–Harris Conjecture, which characterizes the Hilbert functions of homogeneous ideals containing a regular sequence in the polynomial ring.
"Some special cases of the Eisenbud–Green–Harris conjecture." Illinois J. Math. 56 (3) 661 - 675, Fall 2012. https://doi.org/10.1215/ijm/1391178543