Lex-Plus-Powers Conjecture

The lex-plus-powers conjecture asserts that the lex-plus-powers ideal supplied by the Eisenbud-Green-Harris conjecture also bounds the graded Betti numbers of the original quotient. For a homogeneous ideal over a field containing a ring regular sequence of homogeneous polynomials of total degrees , it asserts the existence of such a with the same Hilbert function and

The inequality is required simultaneously for all integers and .