A combinatorial bijection on $k$-noncrossing partitions

Zhicong Lin, Dongsu Kim

For any integer $k\ge 2$, we prove combinatorially the following Euler (binomial) transformation identity $$ \NC_{n+1}^{(k)}(t)=t\sum_{i=0}^n{n\choose i}\NW_{i}^{(k)}(t), $$ where…