Paths in graphs and minimal π-sequences in semigroups

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Abstract

By taking a graph theoretic point of view, the author's theory of minimal sequences in semi groups is generalized to minimal π-sequences, where π is any positive quasi-order on the semi group. This generalization is especially complete when π is a linear quasi-order. Finally some possible future applications to the social sciences are considered.

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The author was supported by a National Science Foundation Graduate Fellowship while doing this work.