# Growth rates of permutation grid classes , tours on graphs , and the spectral radius Journal Item

@inproceedings{Bevan2013GrowthRO, title={Growth rates of permutation grid classes , tours on graphs , and the spectral radius Journal Item}, author={David. Bevan}, year={2013} }

- Published 2013

Monotone grid classes of permutations have proven very effective in helping to determine structural and enumerative properties of classical permutation pattern classes. Associated with grid class Grid(M) is a graph, G(M), known as its “row-column” graph. We prove that the exponential growth rate of Grid(M) is equal to the square of the spectral radius of G(M). Consequently, we utilize spectral graph theoretic results to characterise all slowly growing grid classes and to show that for every… CONTINUE READING

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