Solution of Tutte-Loop Equations

  • Bertrand Eynard
Part of the Progress in Mathematical Physics book series (PMP, volume 70)


In this chapter, we solve the loop equations (Tutte’s equations), we compute explicitly the generating functions counting maps of given genus and boundaries. We are first going to solve them for planar maps with one boundary (the disk, i.e. planar rooted maps), then two boundaries (the cylinder), and then arbitrary genus and arbitrary number of boundaries. The disk case (planar rooted maps) was already done by Tutte [83–85]. Generating functions for higher topologies have been computed more recently [5, 31].


Higher Topology Root Planing Loop Equations Topological Recursion Marked Faces 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Bertrand Eynard
    • 1
  1. 1.CEA Saclay Institut de Physique Théorique (IPHT)Gif sur YvetteFrance

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