An elementary proof of Bevan's theorem on the growth of grid classes of   permutations
  Bevan established that the growth rate of a monotone grid class of permutations is equal to the square of the spectral radius of a related bipartite graph. We give an elementary and self-contained proof of a generalization of this result using only Stirling's Formula, the method of Lagrange multipliers, and the singular value decomposition of matrices. 
Michael Albert and Vincent Vatter
math.CO