Martinez-Savage's inversion-sequence conjecture for 3-nonnesting set partitions

An inversion sequence of length $n$ is a sequence $x=x_1x_2\cdots x_n$ satisfying $0\leq x_i<i$ for all $1\leq i\leq n$. A set partition of $[n]$ is enhanced 3-nonnesting (respectively, enhanced 3-noncrossing) if it contains no enhanced nesting (respectively, crossing) of size $3$. Martinez-Savage's conjecture. Inversion sequences of length $n$ with no weakly decreasing subsequence of length $3$ are equinumerous with enhanced 3-nonnesting (3-noncrossing) set partitions of $[n]$. Lin confirmed this conjecture using generating trees, the obstinate kernel method and Zeilberger's algorithm.