Inequalities for posets

Fedor Petrov
Steklov Institute of Mathematics at St. Petersburg

We discuss several recent inequalities between combinatorial characteristics of posets: hooks and antihooks, chains and antichains, number of linear extensions. Some of them are non-trivial already for Young diagrams. The common tool is majorization theory which I am going to briefly remind. Based on joint works with Igor Pak, Vyacheslav Sokolov and Ivan Bochkov.

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