On some partitions related to \(\mathbb Q(\sqrt 2)\) (Q1010895)

Summary: We offer some new identities for a bipartition function, which has a relation to a Hecke-type identity of Andrews. Further, we show this partition function is lacunary, and relate it to a real quadratic field. Editorial remark: From the review of J. Lovejoy (MR 2475544): All of the main theorems in this paper are incorrect. The author erroneously replaces the term \[ \frac{(zq^ n;q)_ {\infty}}{(1-zq^ {2n})(zq^ {2n+1};q^ 2)_ {\infty}} \] by \((zq^ {2n+2};q^ 2)_ {\infty}\) in the proof of his key identity (4), and this mistake is propagated throughout the paper.