Philippe Dumas's web site

2024	First-order factors of linear Mahler operators. Preprint ArXiv 2403.11545, 2024 with Frédéric CHYZAK, Thomas DREYFUS, Marc MEZZAROBBA, [PDF] , [BibTex] .
2020	A Gröbner-basis theory for divide-and-conquer recurrences. ISSAC'20, pages 99-106, with Frédéric CHYZAK. [PDF] , [BibTex] .
2019	Fast Coefficient Computation for Algebraic Power Series in Positive Characteristic. ANTS–XIII (Thirteenth Algorithmic Number Theory Symposium, 2018), with Alin BOSTAN, Xavier CARUSO, and Gilles CHRISTOL. [PDF] , [BibTex] .
	Becker's conjecture on Mahler functions. Transactions of the American Mathematical Society, in press, with Jason BELL, Frédéric CHYZAK, Michael COONS, [PDF] , [BibTex] .
2018	Computing solutions of linear Mahler equations. Mathematics of Computation, vol. 87, no. 314, p. 2977–3021, 2018, with Frédéric CHYZAK, Thomas DREYFUS, Marc MEZZAROBBA, [PDF] , [BibTex] .
	Fast Computation of the Nth Term of an Algebraic Series over a Finite Prime Field. ISSAC '16 Proceedings, p. 119–126, 2016, with Alin BOSTAN and Gilles CHRISTOL. [PDF] , [BibTex] .
2014	Asymptotic expansions for linear homogeneous divide-and-conquer recurrences: Algebraic and analytic approaches collated. Theoretical Computer Science, vol. 548, p. 25–53, 2014, [PDF] , [BibTex] .
2013	Joint spectral radius, dilation equations, and asymptotic behavior of radix-rational sequences. Linear Algebra and its Applications, vol. 438, p. 2107–2126, 2013. [PDF] , [BibTeX] .
2012	Dr Flajolet's elixir or Mellin transform and asymptotics. Introduction to vol. III, chap. 4 of Philippe Flajolet's Collected Works, [PDF] , References: [PDF] , [BibTex] .
2010	Wronskians and linear independence. American Mathematical Monthly, vol. 117, no. 8, p. 722–727, 2010, with Alin BOSTAN. [PDF] , [BibTex] .
2007	Asymptotic behaviour of a non-commutative rational series with a nonnegative linear representation. Discrete Mathematics & Theoretical Computer Science, vol. 9, no. 1, p. 247–272, 2007, with Helger LIPMAA and Johan WALLÉN. [PDF] , [BibTex] .
2006	Some exactly solvable models of urn process theory. Discrete Mathematics & Theoretical Computer Science, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, p. 59–118, 2006, with Philippe FLAJOLET and Vincent PUYHAUBERT. [PDF] , [BibTex] .
2004	On the Additive Differential Probability of Exclusive-Or. Fast Software Encryption, 11th International Workshop, Lecture Notes in Computer Science, vol. 3017, p. 317–331, 2004, with Helger LIPMAA and Johan WALLÉN. [PDF] , [BibTex] .
2001	A randomized algorithm for approximate string matching. Algorithmica, vol. 29, no. 3, p. 468–486, 2001, with Mike ATALLAH and Frédéric CHYZAK. [PDF] , [BibTex] .
1997	Maple Son bon usage en mathématiques. Springer-Verlag, 1997, with Xavier GOURDON. [BibTex] .
1996	Asymptotique des récurrences mahlériennes : le cas cyclotomique. Journal de Théorie des Nombres de Bordeaux, vol. 8, no. 1, p. 1–30, 1996, with Philippe FLAJOLET. [PDF] , [BibTex] .
1995	Une introduction à Maple. Rapport technique INRIA, no. 173, with Xavier GOURDON. [PDF] , [BibTex] .
	Maple and the Putnam Competition. The Maple Technical Newsletter, vol. 2, no. 2, p. 63–68, 1995, with Bruno SALVY. [PDF] , [BibTex] .
	Random palindromes: multivariate generating function and Bernoulli density. Discrete Mathematics, vol. 139, no. 1-3, p. 143–154, 1995, with Loÿs THIMONIER. [PDF] , [BibTex] .
	Mellin transforms and asymptotics: harmonic sums. Theoretical Computer Science, vol. 144, no. 1-2, p. 3–58, 1995, with Philippe FLAJOLET and Xavier GOURDON. [PDF] , [BibTex] .
1993	Récurrences mahlériennes, suites automatiques, études asymptotiques. Thèse, Université de Bordeaux I, Talence, 1993. [PDF] , [BibTex] .
	Algebraic aspects of B-regular series. Automata, languages and programming (Lund, 1993), LNCS 700, p. 457–468. [PDF] , [BibTex] .
	Additive cellular automata and algebraic series. Theoretical Computer Science, vol. 119, no. 2, p. 345–354, 1993, with Bruce LITOW. [PDF] , [BibTex] .
1989	Suites automatiques à valeurs dans un anneau commutatif. Technical report Laboratoire de Recherche en Informatique, Université Paris-Sud, vol. 535, 1989. [PDF] , [BibTex] .