Dominique Foata

Dominique Cyprien Foata was born on 12 October 1934 in Damascus, then under the French Mandate for Syria and the Lebanon. His father, Jean-Baptiste Foata (1905 to 1985), was a commandant in the French colonial army who, by his son's account, lived six years in Syria, five in French West Africa, three in Indochina and two in Germany. His mother was Geneviève Foata, and he had a brother, Xavier. Family ties also ran to Joigny in Burgundy, where his maternal grandfather worked as a tailor. As a young man he went on ski camps in Austria in 1956 and 1957.

Foata studied mathematics in Paris, where he earned his licence, and prepared a third-cycle doctorate at the Institute of Statistics of the University of Paris (ISUP) under the probabilist Daniel Dugué. He then joined the CNRS. Between 1959 and 1961 he held research posts in the United States, at Ohio State University and at the University of North Carolina at Chapel Hill. In 1965 he defended his State doctorate in Paris, Étude algébrique de certains problèmes d'analyse combinatoire et du calcul des probabilités, under the guidance of Marcel-Paul Schützenberger, whose first doctoral student he was.

In Columbus, Ohio, Foata worked alongside Henry B. Mann and in the statistics laboratory of Donald R. Whitney, and spent a summer on vision research. At Chapel Hill, on a fellowship from R. C. Bose, he wrote a computer program with D. K. Ray-Chaudhuri for constructing projective geometries, published in Communications of the ACM in 1961. Back in France he did his military service in the French Navy's Operations Research Bureau, held a provisional post at Lille in 1964 and joined the University of Strasbourg in October 1965.

His thesis extracted from MacMahon's classical work the two fundamental transformations now named after him, which link excedances to descents and the major index to inversions. With Pierre Cartier he published Problèmes combinatoires de commutation et réarrangements (1969), the origin of the Cartier-Foata or trace monoid, and with Schützenberger he wrote Théorie géométrique des polynômes eulériens (1970). He spent a semester at Stanford in 1971 at Donald Knuth's invitation.

His later work covered permutation statistics, q-analogues of Eulerian polynomials, the combinatorics of tangent and secant numbers, and combinatorial models for special functions and orthogonal polynomials, including a combinatorial proof of the Mehler formula and, with Pierre Leroux, of the generating function for Jacobi polynomials. In 1980 he co-founded the Séminaire Lotharingien de Combinatoire with Adalbert Kerber and Volker Strehl. He led Strasbourg's mathematics and computer science faculty (UFR) from 1989 to 1992. A long late collaboration with Guoniu Han produced many papers, the last listed on his website being The Entringer-Poupard Matrix Sequence, written with Han and Strehl.

While in Columbus in 1959 and 1960 Foata met Anne Laugel, a young Frenchwoman at the Ohio State University hospital. They married on 6 October 1962 and later made frequent visits to the United States, some lasting several months, the last in 2010. They had a daughter, Stéphanie. He lived in Strasbourg for more than sixty years. Colleagues described him as kind, patient and eager to help, a polyglot with a passion for history and geography.

Foata often insisted on the role of luck in research, writing that wanting to find something is not enough and that one must also arrive at the right moment. He considered himself fortunate to have worked under Schützenberger and to have had Pierre Cartier as a co-author. His letters from 1959 to 1961 record his sympathy for Algerian independence, his observations of racial segregation and student boycotts in North Carolina and his pleasure at John F. Kennedy's election. He valued elegant, short combinatorial proofs over heavy machinery, describing his proof of the Mehler formula as not too complicated, and still spectacular.

Foata is counted, with Cartier and Schützenberger, among the founders of the modern approach to classical combinatorics that fed the growth of algebraic combinatorics. The Foata transformation, Foata's transition lemma and the Cartier-Foata monoid are taught in courses on permutations and theoretical computer science. The Séminaire Lotharingien de Combinatoire, which he co-founded, remains a leading open-access venue. His doctoral students and close Strasbourg collaborators included Jacques Désarménien, Dominique Dumont, Jean Françon, Laurent Habsieger, Jiang Zeng, Guoniu Han, Bodo Lass and Arthur Randrianarivony.

Invited speaker, International Congress of Mathematicians, Warsaw (1983). Prix Paul Doistau-Émile Blutet of the French Academy of Sciences (1985). Scientific prize of the Union des Assurances de Paris (1985). Member of the council of the Société Mathématique de France (1983 to 1986). Foata Festschrift volume of the Electronic Journal of Combinatorics (1996). FoataFest conference at Temple University, Philadelphia (2000). Tribute talks by Doron Zeilberger at Rutgers (2014 and 2024) and a surprise party for his ninetieth birthday on 17 October 2024.

Problèmes combinatoires de commutation et réarrangements, with Pierre Cartier (Springer, 1969). Théorie géométrique des polynômes eulériens, with Marcel-Paul Schützenberger (Springer, 1970). La série génératrice exponentielle dans les problèmes d'énumération (Presses de l'Université de Montréal, 1974). Processus stochastiques, with Aimé Fuchs (Dunod, 2002). Calcul des probabilités, with Aimé Fuchs and later Jacques Franchi (Dunod, several editions; German translation by Volker Strehl, 1999). Lettres d'Amérique 1959-61 (Séminaire Lotharingien de Combinatoire, 2026). An interview with him from 17 January 1978 is held in the Eugene Dynkin Collection of Mathematics Interviews at Cornell University Library.

Dominique Foata died in Strasbourg on 30 September 2026, at the age of 91, in his 92nd year. The cause of death has not been made public. His death was announced by the Société Mathématique de France, which published a tribute by his colleague Guoniu Han. A religious service was held on 6 October 2026 at the Church of Saint-Maurice in Strasbourg, followed by burial in the cemetery of Benfeld. He was survived by his wife Anne and his daughter Stéphanie.