The generating function of planar Eulerian orientations

@article{BousquetMlou2018TheGF,
  title={The generating function of planar Eulerian orientations},
  author={Mireille Bousquet-M{\'e}lou and Andrew Elvey Price},
  journal={J. Comb. Theory, Ser. A},
  year={2018},
  volume={172},
  pages={105183}
}
  • Mireille Bousquet-Mélou, Andrew Elvey Price
  • Published in J. Comb. Theory, Ser. A 2018
  • Mathematics, Computer Science
  • The enumeration of planar maps equipped with an Eulerian orientation has attracted attention in both combinatorics and theoretical physics since at least 2000. The case of 4-valent maps is particularly interesting: these orientations are in bijection with properly 3-coloured quadrangulations, while in physics they correspond to configurations of the ice model.We solve both problems -- namely the enumeration of planar Eulerian orientations and of 4-valent planar Eulerian orientations --by… CONTINUE READING

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