The kernel method(s)

In this webpage, I'll try to maintain a list of Maple sessions/datas/pdf for my articles related to the kernel method, and some generalization of it.

• Generating Functions for Generating Trees, C. Banderier, Mireille Bousquet-Mélou, Alain Denise, Philippe Flajolet, Danièle Gardy, Dominique Gouyou-Beauchamps. Discrete Mathematics 246(1-3), March 2002, pp. 29-55 : [ pdf ]
• Basic Analytic Combinatorics of Directed Lattice Paths, C. Banderier, Philippe Flajolet. (June 2001), 39 pages. Theoretical Computer Science. Vol. 281. Issue 1-2, pp. 37-80, Jun. 2002, [ pdf ]
• Limit laws for basic parameters of lattice paths with unbounded jumps, C. Banderier. (Jan. 2002), 15 pages. Second Colloquium on Mathematics and Computer Science. [ pdf ]
• Analytic Combinatorics of Lattice Paths: Enumeration and Asymptotics for the Average Area, C. Banderier, Bernhard Gittenberger. Proceedings of the 4th Colloquium of Mathematics and Computer Science, DMTCS, AG, pp. 345-355. April 1st, 2006 [ pdf ]
• Bounded discrete walks, Cyril Banderier, Pierre Nicodème. In DMTCS Proceedings, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), pp. 35-48, 2010. [ pdf ]
• Some reflections on lattice paths, Cyril Banderier, Michael Wallner. In Proceedings of the 25th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2014), Paris, pages 25-36, 2014. [ pdf ]
• Formulae and Asymptotics for Coefficients of Algebraic Functions, Cyril Banderier, Michael Drmota, Combinatorics, Probability and Computing, volume 24, January 2015, pp 1-53. doi:10.1017/S0963548314000728 [ preprint pdf, journal version pdf ]
• Lattice paths with catastrophes, Cyril Banderier, Michael Wallner. Discrete Mathematics & Theoretical Computer Science, volume 19, #23, September 2017, 31 pages. [ arXiv, journal version ]
• Local time for lattice paths and the associated limit laws, Cyril Banderier, Michael Wallner, 10p., Proceedings of GASCom 2018. [pdf]
• The kernel method for lattice paths below a line of rational slope, Cyril Banderier, Michael Wallner. In Lattice Path Combinatorics and Applications. Developments in Mathematics Series (Springer), pp. 119-154, 2019. [ pdf ]
• Explicit formulas for enumeration of lattice paths: basketball and the kernel method, Cyril Banderier, Christian Krattenthaler, Alan Krinik, Dmitry Kruchinin, Vladimir Kruchinin, David Nguyen & Michael Wallner. In Lattice Path Combinatorics and Applications. Developments in Mathematics Series (Springer), pp. 78-118, 2019. [ pdf ]
• Analytic combinatorics of lattice paths with forbidden patterns, the vectorial kernel method, and generating functions for pushdown automata, Andrei Asinowski, Axel Bacher, Cyril Banderier, Bernhard Gittenberger. Algorithmica. pp. 1-43, 2019. [pdf]
• Generating functions for lattice paths with several forbidden patterns, Andrei Asinowski, Cyril Banderier , Valerie Roitner. Submitted, 2019. [pdf]