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.
Hypergraph Fuss-Catalan Numbers
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abstract
The Catalan numbers $C_n$ are an extremely well-studied sequence of numbers that appear as the answer to many combinatorial problems. Two generalizations of these numbers that have been studied are the Fuss-Catalan numbers and the Hypergraph Catalan numbers. In this paper, we study the combination of these, the Hypergraph Fuss-Catalan numbers. We provide some combinatorial interpretations of these numbers, as well as describe their generating function.
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math.CO 1years
2025 1verdicts
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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.