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In Preprint 1 we write numerical labels 0 or 1 at each vertex of a Dynkin diagram $D$. We call it a labeling of the graph (Dynkin diagram) $D$.

In Preprint 2 we consider an extended (affine) Dynkin diagram $\tilde{D}$. At each vertex of $\tilde{D}$ we write numerical labels 0, 1, or 2 such that a certain integer linear combination of the labels equals 2. We call it a Kac 2-labeling of $\tilde{D}$.

Now I am going to write Preprint 3, where I would like to use both labelings and Kac 2-labelings. I would like to use a better term than "Kac 2-labelings" in order not to confuse the reader.

Question. What synonyms to "Kac 2-labelings" of a graph (affine Dynkin diagram) can I use? Maybe "Kac 2-markings"? Anything else?

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  • $\begingroup$ How about "1-labellings" and "2-labellings" instead of "labellings" and "Kac 2-labellings" respectively? $\endgroup$
    – Boris Bukh
    Commented Sep 26, 2015 at 12:59
  • $\begingroup$ @BorisBukh: No, this does not work. Actually I have Kac $n$-labelings (they classify inner automorphisms of order $n$ of complex simple Lie algebras), and a labeling is not a Kac 1-labeling. $\endgroup$
    – Mikhail Borovoi
    Commented Sep 26, 2015 at 18:26
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    $\begingroup$ How about "marking" and "labeling" ? Or "01-coloring"? $\endgroup$
    – Per Alexandersson
    Commented Sep 26, 2015 at 22:00
  • $\begingroup$ @PerAlexandersson: Thank you! I already have colorings as well, but "labeling" and "marking" will be good! $\endgroup$
    – Mikhail Borovoi
    Commented Sep 27, 2015 at 6:02

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