Abstract
The purpose of this note is to show that a finitely generated graded module M over S = k[x1, …, xn] , k a field, is sequentially Cohen-Macaulay if and only if its arithmetic degree adeg(M) agrees with adeg(F/ginrevlex(U)) , where F is a graded free S-module and M ≅ F/U . This answers positively a conjecture of Lu and Yu from 2016.