Generating functionology
Regressive Ramsey numbers are Ackermannian
Journal of Combinatorial Theory Series A
An Ackermannian Polynomial Ideal
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
An extremely sharp phase transition threshold for the slow growing hierarchy
Mathematical Structures in Computer Science
Phase Transitions for Weakly Increasing Sequences
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
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In this paper we first survey recent advances on phase transition phenomena which are related to natural subclasses of the recursive functions. Special emphasis is put on descent recursive functions, witness bounding functions for well-partial orders and Ramsey functions. In the last section we prove in addition some results which show how the asymptotic of the standard Ramsey function is affected by phase transitions for associated parameterized Ramsey functions.