A NOTE ON FINITE MULTISETS WITH COINCIDING REPRESENTATION FUNCTIONS
Zhenhua Qu · Bulletin of the Australian Mathematical Society · 2026
Abstract We study a pair of finite multisets of nonnegative integers which have coinciding representation functions. We show that there is a close connection to factorisation of polynomials into cyclotomic polynomials. As an application, we give a complete characterisation of pairs of such sets whose union is the interval $[0,m]$ with two elements removed.