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Leonhard Euler's 1751 correspondence already studied triangulations of a convex polygon and gave a closed formula for their counts. Johann Andreas von Segner supplied a combinatorial recurrence relation in a paper written in 1758. Eugène Charles Catalan's nineteenth-century work connected the formula to bracketed products. This history, documented in Igor Pak's account, shows how the same counting structure reappeared through different objects; the modern name alone does not establish discovery priority.^[ref]

By Igor Pak.

Online text: arxiv.org/pdf/1408.5711

Standalone historical preprint, arXiv:1408.5711. Version 1 was submitted on 25 August 2014; the inspected version 2 is dated 27 August 2014. Its cover says the account will appear as an appendix in a forthcoming book by Richard P. Stanley; the authorship here applies to this preprint, not to the whole book.

Cited passages: §§2–3 and §5, printed pp. 2–4: Euler correspondence, Segner recurrence and Catalan's bracketed products.