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Let $[n]:=\{1,\cdots,n\}$. It is known that $\{\log(p) \mid p \text{ is prime }\}$ is linearly independent over $\mathbb{Q}$. For a subset $A \subset [n]$ we can consider the matrix $L(A):=(\log(x) \...

In A cell complex in number theory by Anders Björner, 2011 a number theoretic cell complex is described which has the property that the Euler characteristic is related to the Mertens function: $$M(n) =...