Research Output per year

### Abstract

Geometric grid classes of permutations have proven to be key in investigations of classical permutation pattern classes. By considering the representation of gridded permutations as words in a trace monoid, we prove that every geometric grid class has a growth rate which is given by the square of the largest root of the matching polynomial of a related graph. As a consequence, we characterise the set of growth rates of geometric grid classes in terms of the spectral radii of trees, explore the influence of "cycle parity" on the growth rate, compare the growth rates of geometric grid classes against those of the corresponding monotone grid classes, and present new results concerning the effect of edge subdivision on the largest root of the matching polynomial.

Original language | English |
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Pages (from-to) | 1-17 |

Number of pages | 17 |

Journal | The Electronic Journal of Combinatorics |

Volume | 21 |

Issue number | 4 |

Publication status | Published - 4 Dec 2014 |

### Keywords

- permutations
- permutation grid classes
- matching polynomial
- growth rates

## Fingerprint Dive into the research topics of 'Growth rates of geometric grid classes of permutations'. Together they form a unique fingerprint.

## Research Output

- 4 Citations
- 1 Doctoral Thesis

## On the growth of permutation classes

Bevan, D., 1 Jun 2015, Milton Keynes.Research output: Thesis › Doctoral Thesis