13 citations · 41 across the 10 of their papers we have counts for
13 papers
Families of Eliahou semigroups linked to Farey intervals
Axel Bacher
We describe a way to explore the numerical semigroup tree to find all Eliahou semigroups of conductor up to 200 (and conjecturally up to 400) thanks to a new way of representing th…
Progressive and Rushed Dyck Paths
Axel Bacher
We call progressive paths and rushed paths two families of Dyck paths studied by Asinowski and Jelinek, which have the same enumerating sequence (OEIS entry A287709). We present a…
Improving the Florentine algorithms: recovering algorithms for Motzkin and Schröder paths
Axel Bacher
We present random sampling procedures for Motzkin and Schröder paths, following previous work on Dyck paths. Our algorithms follow the anticipated rejection method of the Florentin…
A new bijection on m-Dyck paths with application to random sampling
Axel Bacher
We present a new bijection between variants of -Dyck paths (paths with steps in starting and ending at height and remaining at non-negative height), which genera…
Continued Classification of 3D Lattice Walks in the Positive Octant
Axel Bacher, Manuel Kauers, Rika Yatchak
We continue the investigations of lattice walks in the three dimensional lattice restricted to the positive octant. We separate models which clearly have a D-finite generating func…
Complexity of Anticipated Rejection Algorithms and the Darling-Mandelbrot Distribution
Axel Bacher, Andrea Sportiello
We study in limit law the complexity of some anticipated rejection random sampling algorithms. We express this complexity in terms of a probabilistic process, the threshold sum pro…