Investigation of Grothendieck groups in n-cluster categories shows generalization of previous results.
In this paper, we investigate the Grothendieck groups [Formula: see text] of [Formula: see text]-cluster categories [Formula: see text] of type [Formula: see text] introduced by Holm and Jørgensen. We prove that [Formula: see text] for an arbitrary [Formula: see text]. As an application, this generalizes a result of Murphy for [Formula: see text].
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Huimin Chang (2026) studied this question.
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