Set Partitions with Forbidden Patterns

William Y. C. Chen
Center for Combinatorics, Nankai University, Tianjin 300071, P.R. China
chen@nankai.edu.cn

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We review some recent work Eva Y. P. Deng, Rosena R. X. Du, Richard Stanley, Catherine H. F. Yan on set partitions with forbidden patterns, especially, on the bijection between k-noncrossing matchings and k-nonnesting matchings by using oscillating tableaux. Recent developments in this direction will be reported including the work of Martin Klazar, Mireille Bousquet-Melou and Guoce Xin, Christian Krattenthaler, and Sylvie Corteel.