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Classification of monomial Rota-Baxter operators on k[x]

Rota-Baxter operators were introduced to solve certain analytic and combinatorial problems and then applied to many fields in mathematics and mathematical physics. The polynomial algebra $\mathbf{k}[x]$ plays a central role both in analysis and algebra. In this paper, we explicitly classified all monomial Rota-Baxter operators on $\mathbf{k}[x]$.