Abstract
We attach Mahler measures to digraphs and find combinatorial realizations of nearly all of the known low-degree ( ) small (< 1.3) one-variable Mahler measures. We find one new such measure not on either of the lists maintained by Mossinghoff and Sac-Épée. Considering limits of sequences of measures attached to families of digraphs, we get combinatorial explanations for 57 of the 61 known irreducible two-variable measures below 1.37.
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Acknowledgments
We are extremely grateful for the careful reading of the manuscript by the referees, and for their helpful suggestions.
Declaration of Interest
No potential conflict of interest was reported by the author(s).