[Merged by Bors] - feat(combinatorics/catalan): Connection between Catalan numbers and number of trees #16583
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…ty/mathlib into catalan_numbers_trees
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Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
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| /-- A finset of all trees with `n` nodes. See `mem_trees_of_nodes_eq` -/ | ||
| def trees_of_num_nodes_eq : ℕ → finset (tree unit) | ||
| | 0 := {nil} | ||
| | (n+1) := (finset.nat.antidiagonal n).attach.bUnion $ λ ijh, |
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@YaelDillies, can you see a way to use disj_Union here instead?
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Nevermind, this can wait till a follow-up
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I thought about it but it doesn't seem obvious at all.
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…umber of trees (#16583) Shows that the number of binary trees with `n` nodes is the `n`th Catalan number.
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Shows that the number of binary trees with
nnodes is thenth Catalan number.tree unit#16715