Eulerian orientations and the six-vertex model on planar maps

Résumé : We address the enumeration of planar 4-valent maps equipped with an Eulerian orientation by two different methods, and compare the solutions we thus obtain. With the first method we enumerate these orientations as well as a restricted class which we show to be in bijection with general Eulerian orientations. The second method, based on the work of Kostov, allows us to enumerate these 4-valent orienta-tions with a weight on some vertices, corresponding to the six vertex model. We prove that this result generalises both results obtained using the first method, although the equivalence is not immediately clear.
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Submitted on : Tuesday, November 5, 2019 - 9:59:12 AM
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Mireille Bousquet-Mélou, Andrew Price, Paul Zinn-Justin. Eulerian orientations and the six-vertex model on planar maps. Formal Power Series and Algebraic Combinatorics, Jul 2019, Ljlubljana, Slovenia. ⟨hal-02346701⟩

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