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.
Flattened Catalan Words
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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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math.CO 1years
2025 1verdicts
REJECT 1representative citing papers
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Symmetry in Tree Parking Distributions
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.