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Seminar
FIELD Math: CMC
DATE August 20 (Tue), 2019
TIME 11:00-12:00
PLACE 8309
SPEAKER Dongsu Kim
HOST Koh, Kyewon
INSTITUTE KAIST
TITLE A combinatorial bijection on $k$-noncrossing partitions
ABSTRACT This talk is meant to give a combinatorial experience to noncombinatorialists. For any integer $k\geq2$, we prove combinatorially the following transformation identity $$ \NC_{n+1}^{(k)}(t)=t\sum_{i=0}^n{n\choose i}\NW_{i}^{(k)}(t), $$ where $\NC_{m}^{(k)}(t)$ (resp.~$\NW_{m}^{(k)}(t)$) is the enumerative polynomial on partitions of $\{1,\ldots,m\}$ avoiding $k$-crossings (resp.~enhanced $k$-crossings) by number of blocks.
It is based on my preprint (arXiv:1905.10526) with Zhicong Lin.
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