Stable homology isomorphisms for the partition and Jones annular algebras

We show that the homology of the Jones annular algebras is isomorphic to that of the cyclic groups below a line of gradient \(\frac{1}{2}\) $\frac{1}{2}$ . We also show that the homology of the partition algebras is isomorphic to that of the symmetric groups below a line of gradient 1, strengthening a result of Boyd–Hepworth–Patzt. Both isomorphisms hold in a range exceeding the stability range of the algebras in question. Along the way, we prove the usual odd-strand and invertible parameter results for the Jones annular algebras.