In recent years, the techniques of analytic combinatorics in several variables (ACSV) have been applied to determine asymptotics for several families of lattice path models restricted to the orthant \({\mathbb {N}}^d\) and defined by step sets \({\mathcal {S}}\subset \{-1,0,1\}^d\setminus \{\textbf{0}\}\) . Using the theory of ACSV for smooth singular sets, Melczer and Mishna determined asymptotics for the number of walks in any model whose set of steps \({\mathcal {S}}\) is ‘highly symmetric’ (symmetric over every axis). Building on this work, Melczer and Wilson determined asymptotics for all models where \({\mathcal {S}}\) is ‘mostly symmetric’ (symmetric over all but one axis) except for models whose set of steps have a vector sum of zero but are not highly symmetric. In this paper, we complete the asymptotic classification of the mostly symmetric case by analyzing a family of saddle-point-like integrals whose amplitudes are singular near their saddle points.
