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{\bf Leonard J. Schulman}
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{\bf The Quantifier Semigroup for Bipartite Graphs}
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In a bipartite graph there are two widely encountered
monotone mappings from subsets of one side of the graph to
subsets of the other side: one corresponds to the quantifier
``there exists a neighbor in the subset'' and the other to
the quantifier ``all neighbors are in the subset.'' These
mappings generate a partially ordered semigroup which we
characterize in terms of ``run-unimodal'' words.

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