Determine the generating function for Class 1953A

Determine the generating function for inversion sequences avoiding the relation triple $(-,>,>)$, equivalently the patterns $(110,120,210)$, and establish whether the generating function is algebraic.

Background

Class 1953A consists of inversion sequences avoiding $(110,120,210)$ and is Wilf-equivalent to Class 1953B, which avoids $(100,120,210)$. The paper gives a left-growing succession rule indexed by the lengths of two consecutive zero runs and derives a compact functional equation for the generating function.

The functional equation is not solved in the paper. The authors also conjecture that the generating function is not algebraic, so an exact solution and rigorous determination of its algebraic nature remain unresolved.