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Explore the intricacies of combinatorial inequalities and interpretations in this third installment of a seminar series presented by Igor Pak at the Institute for Advanced Study. Delve into inequalities for linear extensions of finite posets, beginning with examples that possess combinatorial proofs. Examine Stanley's inequality and understand why its defect lacks a combinatorial interpretation. If time allows, investigate the implications for equality cases and stability of the Alexandrov-Fenchel inequality. This talk, part of a joint work with Swee Hong Chan (STOC 2024), offers advanced insights into combinatorial mathematics and its applications.
