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\title{\bf Corrigendum to: Frank a Campo, Relations between Powers of Dedekind Numbers and Exponential Sums Related to Them, JIS Vol. 21 (2018), Article 18.4.4}
\author{\sc Frank a Campo}
\date{\small Seilerwall 33, D 41747 Viersen, Germany\\
{\sf acampo.frank@gmail.com}}

\maketitle

The conditions of Lemma 8(a) must read (corrections in {\bf bold}):
\newline

{\em Let $P_1, P_2$, and $Q$ be non-empty finite or infinite posets, $X_1$ the carrier of $P_1$, $X_2$ the carrier of $P_2$.

(a) Let $\phi : P_1 \rightarrow P_2$ be a bijective homomorphism. Then
\begin{align*}
\Phi : \H(P_2, Q) & \rightarrow \H(P_1, Q), \\
\xi & \mapsto \xi \circ \phi
\end{align*}
is a one-to-one homomorphism. If $Q$ is not an antichain, then $\Phi$ is onto (and an isomorphism) iff $\phi$ is an isomorphism. {\bf For $\bf Q \simeq A_1$, $\bf \Phi$ is onto. If $\bf Q \not\simeq A_1$ } is an antichain, then $\Phi$ is onto iff the induced mapping
\begin{align*}
\phi' : \mysetdescr{ \gamma_{P_1}(x) }{ x \in X_1 } & \rightarrow \mysetdescr{ \gamma_{P_2}(z) }{ z \in X_2 } \\
\gamma_{P_1}(x) & \mapsto \gamma_{P_2}(\phi(x))
\end{align*}
is one-to-one. }

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