In the paper under review the author describes the degenerations of monomial ideals in \(K[[x,y]]\) with \(\text{ Aut}(K[[x,y]])\)-orbit of dimension at most \(3\). In particular, she determines the monomial ideals that any power of \((x,y^4)\) can degenerate to and makes a conjecture about all the ideals that the powers of \((x,y^4)\) can degenerate to. She also gives some numerical evidence linking the characteristics in which one ideal degenerates to another with the enumeration of lattice paths.