Explicit formulas and asymptotic bounds are derived for the counts of countable homogeneous colored linear orderings in k colors and C_{n,m}-homogeneous linear orderings by mapping them to finite combinatorial objects.
Macpherson,A survey of homogeneous structures, Discrete Math.311(2011), no
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Enumerative Combinatorics of Homogeneous Linear Orderings
Explicit formulas and asymptotic bounds are derived for the counts of countable homogeneous colored linear orderings in k colors and C_{n,m}-homogeneous linear orderings by mapping them to finite combinatorial objects.