In this paper, we deal with plane curves with cusps. It is well known that there are various types of cusps. Among them, we investigate criteria for $(n, n+1)$ cusps with respect to several differential conditions and relations between these singularities and evolutes of fronts. We give complete classifications with respect to $(4, 5)$-cusps.
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Yoshiki Matsushita (2024) studied this question.
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