Borel-plus-powers monomial ideals

Abstract

Let S = K [ x 1 , … , x n ] be a standard graded polynomial ring over a field K . 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 x 1 p , … , x n p , where p is a prime number.