Expansion of polynomial Lie group integrals in terms of certain maps on   surfaces, and factorizations of permutations
  Using the diagrammatic approach to integrals over Gaussian random matrices, we find a representation for polynomial Lie group integrals as infinite sums over certain maps on surfaces. The maps involved satisfy a specific condition: they have some marked vertices, and no closed walks that avoid these vertices. We also formulate our results in terms of permutations, arriving at new kinds of factorization problems. 
Marcel Novaes
math-ph math.CO math.GR math.MP