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Random generation algorithm reveals properties of k-coloured Motzkin paths, indicating new connections in combinatorics.
We study k-coloured Motzkin paths, namely Motzkin paths in which horizontal steps can be coloured in k different ways, and investigate their connection with the number of prefixes ending at odd height from both an analytical and a combinatorial point of view.Moreover, the combinatorial approach provides a random generation algorithm for k-coloured Motzkin paths in linear-time.
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Barcucci et al. (2026) studied this question.
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