### $(-1)$-enumeration of self-complementary plane partitions.

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An infinite word is $S$-automatic if, for all $n\ge 0$, its $(n+1)$st letter is the output of a deterministic automaton fed with the representation of $n$ in the considered numeration system $S$. In this extended abstract, we consider an analogous definition in a multidimensional setting and present the connection to the shape-symmetric infinite words introduced by Arnaud Maes. More precisely, for $d\ge 2$, we state that a multidimensional infinite word $x:{\mathbb{N}}^{d}\to \Sigma $ over a finite alphabet $\Sigma $ is $S$-automatic for some abstract numeration...