Note explores representation functions of finite multisets, revealing polynomial connections.
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.
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Zhenhua Qu (2026) studied this question.
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