Hayman Admissible Functions in Several Variables

Abstract

An alternative generalisation of Hayman's concept of admissible functions to functions in several variables is developed and a multivariate asymptotic expansion for the coefficients is proved. In contrast to existing generalisations of Hayman admissibility, most of the closure properties which are satisfied by Hayman's admissible functions can be shown to hold for this class of functions as well.

Enumeration of Generalized $BCI$ Lambda-terms

“…When studying not only the size but further properties of BCK(p)-terms by means of multivariate generating functions, the above remarks suggest that these functions will be (multivariate) Hayman-admissible such that a multivariate saddle point method applies (cf. [7]).…”

Asymptotic Distribution of Parameters in Trivalent Maps and Linear Lambda Terms

“…converges in all L p spaces, with p ∈ [1, +∞), to 1/l and remarks that an approach based on analytic combinatorics may useful in obtaining the limit distributions of dilations of the random variables N l (σn)/n l/d −1/l. Indeed, our approach yields such limit laws for the cases where A = {1, 2} or A = {1, 3} and in principle can be extended to any finite A, since in all such cases the resulting functions are e-admissible and therefore admit Gaussian limit laws as shown in [33].…”

Cuts in Increasing Trees

“…We are going to apply multivariate saddle point analysis to evaluate [y i z j ]M (y, z). Precisely, we are going to deal with the generalisation of H-admissibility defined in [GM06]. Indeed, it is easy to show using the closure properties that the functions M (y, z) :=…”