Asymptotics for the number of walks in a Weyl chamber of type \(B\) (Q2925525)

The paper under review is about the determination of the number of lattice paths that stay within a certain fixed region. The author considers the region which is a Weyl chamber of type \(B_k\). The solution given by \textit{D. André} [``Solution directe du problème résolu par M. Bertrand'', C. R., Math., Acad. Sci. Paris 105, 436--737 (1887)] to this problem is repeated. In Lemma 2.1, a generalized reflection principle that applies to walks consisting of steps that are sequences of such atomics steps is stated.NEWLINENEWLINENEWLINEThe main results of the paper under review are Theorems 5.1 and 6.1 in which asymptotic formulas for the total number of walks of length \(n\) with either a fixed or a free end point for a general class of walks as \(n\) tends to infinity.NEWLINENEWLINE In the proofs, the author uses a generating function approach to express the number of walks that he is interested in as a certain coefficient in a specific Laurent polynomial. Then, this coefficient is expressed as a Cauchy integral and asymptotics with the help of saddle point techniques are extracted.