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
JF - The Electronic Journal of Combinatorics
SN - 1077-8926
IS - 4
ER -