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on Tableaux problem 19

The statement

19.[Stan2012a]*Ch. 3 Exer. 135(b) Let $\Lambda_{n}$ be the set of all $p(n)$ partitions of the integer $n\geq 0$ . Order $\Lambda_{n}$ by refinement. Determine the Möbius function $\mu(\lambda,\rho)$ of $\Lambda_{n}$ . (This is trivial when $\lambda=\left<1^{n}\right>$ and easy when $\lambda=\left<1^{n-2}2^{1}\right>$ .)

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.