Integral positive (negative) quandle cocycle invariants are trivial for knots

In this note we prove that for any finite quandle $X$ and any 2-cocycle $ϕ\in Z^2_{Q\pm}(X; \mathds{Z})$, the cocycle invariant $Φ^{\pm}_ϕ(K)$ is trivial for all knots $K$.

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