The paper proves the Pons-Batle conjecture for bounded reticulation number k via explicit bijections to Young tableaux with walls and holes, derives closed-form recurrences, and shows Beta(2,1), Beta(1,2), and Uniform limit laws for k=1 structural parameters.
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A Combinatorial Framework for the Pons-Batle Identity: Young Tableaux, Lattice Paths, and Limit Laws
The paper proves the Pons-Batle conjecture for bounded reticulation number k via explicit bijections to Young tableaux with walls and holes, derives closed-form recurrences, and shows Beta(2,1), Beta(1,2), and Uniform limit laws for k=1 structural parameters.