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I'd like to know who is the first person that introduced the tree of phrase structure in linguistics.

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"Tree" has been a thing in mathematics for some time. "Phrase structure" is a particular mathematical theory of syntax introduced by Chomsky. As far as I know the first phrase structure tree is on p. VI-205 (268) of "The logical structure of linguistic theory" (1955: original version), where he explains the "Q-derivation" (VI-203a) with a diagram, recognizable as the derivation of some strings (words could be used by he used "c1 c2 c3 c4" etc). The same analysis is given in his dissertation Transformational analysis, a reduction to essentials of part of LSLT. It depends on whether you mean "both tree, and PS analysis". Tree diagramming is older.

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The French linguist Lucien Tesnière also used trees (called stemmas if I remember well). He has nothing to do with Chomsky, and is possibly older. I don't know if he inherited the idea of stemmas from somebody else. https://en.wikipedia.org/wiki/Lucien_Tesni%C3%A8re#Stemmas

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