Dominique Foata

Dominique Foata
Born	(1934-10-12) October 12, 1934 Damascus, French Syria
Nationality	French
Alma mater	University of Paris
Known for	Foata's transition lemma Cartier–Foata matrices Traces
Awards	Prix Paul Doistau–Émile Blutet (1985) ICM Speaker (1983)
Scientific career
Fields	Mathematics
Institutions	University of Strasbourg
Doctoral advisor	Marcel-Paul Schützenberger Daniel Dugué

Dominique Foata (born October 12, 1934) is a mathematician who works in enumerative combinatorics. With Pierre Cartier and Marcel-Paul Schützenberger he pioneered the modern approach to classical combinatorics, that lead, in part, to the current blossoming of algebraic combinatorics. His pioneering work on permutation statistics, and his combinatorial approach to special functions, are especially notable.

Foata gave an invited talk at the International Congress of Mathematicians in Warsaw (1983). Among his honors are the Scientific Prize of the Union des Assurances de Paris (September 1985). With Adalbert Kerber and Volker Strehl he founded the mathematics journal Séminaire Lotharingien de Combinatoire. He is also one of the contributors of the pseudonymous collective M. Lothaire. In 1985, Foata received the Prix Paul Doistau–Émile Blutet.

He was born in Damascus while it was under French mandate.

Selected publications

Books

• with Pierre Cartier : Problèmes combinatoires de commutation et réarrangements, Lecture Notes in Mathematics, volume 85, Springer Verlag, 1969. (Réédition électronique avec trois nouveaux appendices, by D. Foata, B. Lass & Ch. Krattenthaler.)
• with Marcel-Paul Schützenberger : Théorie géométrique des polynômes eulériens, Lecture Notes in Mathematics, volume 138, Springer Verlag, 1970. (Réédition électronique.)
• La série génératrice exponentielle dans les problèmes d'énumération, Les Presses de l´Université de Montreal, 1974.
• with Aimé Fuchs : Processus stochastiques, Dunod, 2002.
• with Jacques Franchi et Aimé Fuchs : Calcul des probabilités, 3^e édition, Dunod, 2012. (translated into German under the title Wahrscheinlichkeitsrechnung, by Volker Strehl. Birkhäuser Verlag AG, 1999.)

Articles

• Foata, Dominique (1968). "On the Netto inversion number of a sequence". Proc. Amer. Math. Soc. 19: 236–240. doi:10.1090/s0002-9939-1968-0223256-9. MR 0223256. S2CID 120818407.
• Foata, Dominique (1981). "Further divisibility properties of theq-tangent numbers". Proc. Amer. Math. Soc. 81 (1): 143–148. doi:10.1090/s0002-9939-1981-0589157-8. MR 0589157.
• with Pierre Leroux: Foata, Dominique; Leroux, Pierre (1983). "Polynômes de Jacobi, interprétation combinatoire et fonction génératrice". Proc. Amer. Math. Soc. 87 (1): 47–53. doi:10.2307/2044349. JSTOR 2044349. MR 0677229.
• with Doron Zeilberger: Foata, Dominique; Zeilberger, Doron (1999). "A combinatorial proof of Bass's evaluations of the Ihara-Selberg zeta functions for graphs". Trans. Amer. Math. Soc. 351 (6): 2257–2274. arXiv:math/9806037. doi:10.1090/s0002-9947-99-02234-5. MR 1487614. S2CID 6868812.
• with Guo-Niu Han: Foata, Dominique; Han, Guo-Niu (2007). "Signed words and permutations, I: A fundamental transformation". Proc. Amer. Math. Soc. 135 (1): 31–40. doi:10.1090/s0002-9939-06-08436-x. MR 2280171.
• with Guo-Niu Han: Foata, Dominique; Han, Guo-Niu (2010). "The q-tangent and q-secant numbers via basic Eulerian polynomials" (PDF). Proc. Amer. Math. Soc. 138 (2): 385–393. doi:10.1090/s0002-9939-09-10144-2. MR 2557155.

See also

• MacMahon's master theorem
• Symbolic method (combinatorics)

External links

• Dominique Foata at the Mathematics Genealogy Project
• Foata's website Archived 2008-02-25 at the Wayback Machine
• the Foata festschrift at the Electronic Journal of Combinatorics, 1996
• Interview with Foata (January 17, 1978, Solana Beach, CA), Eugene Dynkin Collection of Mathematics Interviews, Cornell University Library.