• 충청수학회지
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• 제35권4호
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• pp.335-343
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• 2022

We show that valleys, high peaks, and modular ascents are statistics of Fuss-Catalan paths having a distribution given by the Fuss-Narayana number. We prove the results using the Cycle Lemma and provide bijections among them. We also show that relative peaks are independent of the base path. In particular, valleys and high peaks can be obtained from relative peaks by fixing the base path in certain ways.