  In this paper we study a relation between the cohomology ring of a regular
nilpotent Hessenberg variety and Schubert polynomials. To describe an explicit
presentation of the cohomology ring of a regular nilpotent Hessenberg variety,
polynomials $f_{i,j}$ were introduced by Abe-Harada-Horiguchi-Masuda. We show
that every polynomial $f_{i,j}$ is an alternating sum of certain Schubert
polynomials.
