Borel-plus-powers monomial ideals

Let S=K[x1,…,xn]S=K[x1,…,xn] be a standard graded polynomial ring over a field KK. In this paper, we show that the lex-plus-powers ideal has the largest graded Betti numbers among all Borel-plus-powers monomial ideals with the same Hilbert function. In addition in the case of characteristic 0, by using this result, we prove the lex-plus-powers conjecture for graded ideals containing x1p,…,xnp, where pp is a prime number.