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From geometry to generating functions: rectangulations and permutations (2401.05558v2)
Published 10 Jan 2024 in cs.DM, cs.CG, cs.FL, and math.CO
Abstract: We enumerate several classes of pattern-avoiding rectangulations. We establish new bijective links with pattern-avoiding permutations, prove that their generating functions are algebraic, and confirm several conjectures by Merino and M\"utze. We also analyze a new class of rectangulations, called whirls, using a generating tree.
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