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Shuffle-Compatible Permutation Statistics

Yan Zhuang, Brandeis University
Wednesday, February 21, 2018 - 3:30pm
PDL C-401

It has been observed since the early work of Richard Stanley that several well-known permutation statistics are "compatible" with the operation of shuffling permutations. In joint work with Ira Gessel, we formalize this notion of a shuffle-compatible permutation statistic and initiate an in-depth study of shuffle-compatibility, which has close connections to the theory of P-partitions, quasisymmetric functions, and noncommutative symmetric functions. In this talk, I will survey the main results of our work as well as several new directions of research concerning shuffle-compatibility.

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