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Flattened Catalan Words

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arxiv 2405.05357 v1 pith:7GHHAF6K submitted 2024-05-08 math.CO

Jean-Luc Baril , Pamela E. Harris , José L. Ramírez This is my paper · ORCID
classification math.CO
keywords catalanwordsascentsflattenedpeaksrunsvalleysdescents
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abstract

In this work, we define flattened Catalan words as Catalan words whose runs of weak ascents have leading terms that appear in weakly increasing order. We provide generating functions, formulas, and asymptotic expressions for the number of flattened Catalan words based on the number of runs of ascents (descents), runs of weak ascents (descents), $\ell$-valleys, valleys, symmetric valleys, $\ell$-peaks, peaks, and symmetric peaks.

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Cited by 1 Pith paper

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  1. Symmetry in Tree Parking Distributions

    math.CO 2025-08 reject novelty 6.0 of 10

    Tree parking distributions on m-regular caterpillars yield a q,t-Fuss-Catalan generating function in which the lucky-car and first-spot statistics have a symmetric joint distribution.

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