Combinatorial classes T that are recursively defined using combinations of the standard multiset, sequence, directed cycle and cycle constructions , and their restrictions, have generating series T(z) with a positive radius of convergence; for most of these a simple test can be used to quickly show that the form of the asymptotics is the same as that for… (More)
The Sandwich Theorems proved in this paper give a new method to show that the partition function a(n) of a partition identity A(x) := ∞ n=0 a(n)x n = ∞ n=1 (1 − x n) −p(n) satisfies the condition RT 1 lim n→∞ a(n − 1) a(n) = 1. This leads to numerous examples of naturally occuring classes of relational structures whose finite members enjoy a logical 0–1 law.
We determine precisely those locally finite varieties of unary algebras of finite type which, when augmented by a ternary discriminator, generate a variety with a decidable theory.
Characteristic points have been a primary tool in the study of a generating function defined by a single recursive equation. We investigate the proper way to adapt this tool when working with multi-equation recursive systems.
If F(x) = e G(x) , where F(x) = f (n)x n and G(x) = g(n)x n , with 0 ≤ g(n) = O n θn /n! , θ ∈ (0, 1), and gcd n : g(n) > 0 = 1, then f (n) = o(f (n − 1)). This gives an answer to Compton's request in Question 8.3  for an " easily verifiable sufficient condition " to show that an adequate class of structures has a labelled first-order 0–1 law, namely it… (More)
Let F 1 ,. .. , F k be finite fields with distinct characteristics. We give a finite set of equations which axiomatize the equational theory of F 1 ,. .. , F k and then use these axioms to find a finite AC-term rewrite system which is complete for this theory. In particular this gives finite complete AC-term rewrite systems for many instances of x m ≈ x… (More)