### Abstract

Language | English |
---|---|

Pages | 1-17 |

Number of pages | 17 |

Journal | The Electronic Journal of Combinatorics |

Volume | 21 |

Issue number | 4 |

Publication status | Published - 4 Dec 2014 |

### Fingerprint

### Keywords

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

### Cite this

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*The Electronic Journal of Combinatorics*, vol. 21, no. 4, pp. 1-17.

**Growth rates of geometric grid classes of permutations.** / Bevan, David.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Growth rates of geometric grid classes of permutations

AU - Bevan, David

PY - 2014/12/4

Y1 - 2014/12/4

N2 - 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.

AB - 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.

KW - permutations

KW - permutation grid classes

KW - matching polynomial

KW - growth rates

UR - http://www.combinatorics.org/

M3 - Article

VL - 21

SP - 1

EP - 17

JO - The Electronic Journal of Combinatorics

T2 - The Electronic Journal of Combinatorics

JF - The Electronic Journal of Combinatorics

SN - 1077-8926

IS - 4

ER -