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This note is based on the original proof of the shuffle conjecture byCarlsson and Mellit (arXiv:1508.06239, version 2), which seems to be tooconcise for the combinatorial community. James Haglund spent a semester tocheck through the proof line by line and took explicit note. Guoce Xin wasasked by Adriano Garsia to elaborate the proof. The whole paper is thoroughlychecked and filled in with details. Section 1 and the abstract of the originalpaper is included. Section 2 is rewritten for clarity. Other sections arefilled with detailed proof and computation. We hope this note is accessible tograduate students.

Lecture notes on the Carlsson-Mellit proof of the shuffle conjecture