An elementary proof of Bevan's theorem on the growth of grid classes of permutations
Combinatorics
2017-10-12 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1608.06967,
title = {An elementary proof of Bevan's theorem on the growth of grid classes of permutations},
author = {Michael Albert and Vincent Vatter},
journal= {arXiv preprint arXiv:1608.06967},
year = {2017}
}