Enumeration of $(k,2)$-noncrossing partitions

Abstract

A set partition is said to be $(k,d)$-noncrossing if it avoids the pattern $\mathrm{12...}k\mathrm{12...}d$. We find an explicit formula for the ordinary generating function of the number of $(k,d)$-noncrossing partitions of $\{1,2,...,n\}$ when $d=1,2$.

9 pages, 1 table