# 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} }

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

Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

#### Citations

##### Publications citing this paper.

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 54 REFERENCES

## Counting planar Eulerian orientations

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Spanning forests in regular planar maps

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Planar Maps as Labeled Mobiles

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## The six-vertex model on random lattices

VIEW 8 EXCERPTS

HIGHLY INFLUENTIAL

## BIPOLAR ORIENTATIONS ON PLANAR MAPS AND SLE

VIEW 1 EXCERPT

## The Looping Rate and Sandpile Density of Planar Graphs

VIEW 1 EXCERPT

## Uniform infinite planar quadrangulations with a boundary

VIEW 1 EXCERPT