It's a pleasure for me to be here and to join all of you in wishing a happy birthday to Dominique Foata. Dominique - please stand for a moment, to accept our congratulations. A few weeks ago I was at the University of Illinois, to join a conference that was wishing a happy 80th birthday to Paul Bateman, whom I have also known for many years.
Of course a 65th birthday is quite different from an 80th, because, --, well, there are a lot of differences. Well, it's obvious what they are so I won't bother to list them.
I met Dominique and Anne for the first time in the late 1970's at a Table Ronde in combinatorics at Strasbourg. It was a fine conference, but I must confess that after 20-odd years although I don't remember too many of the talks at the conference, I do remember in detail the dinner that Anne and Dominique served to the conference guests, very graciously, at their home.
The Table Ronde was perhaps the inspiration for its renowned successor, the Séminaire Lotharingien de Combinatoire, which was founded by Dominique, together with Adelbert Kerber and Volker Strehl, in 1980, and which has occupied much of his energy for the past for the past twenty years.
And what, you might ask, is Lotharingien about this Séminaire? Well Lotharingia was a portion of present day Europe, in fact of western Europe. Its origin and boundaries can be traced as follows.
By the treaty of Verdun (A.D. 843), the three sons of the Carolingian emperor "Louis I the Pious" divided the Frankish territory into three parts: Francia Occidentalis went to "Charles II the Bald," Francia Orientalis to "Louis the German," and Francia Media, the zone extending from the Low Countries to Italy, to the emperor Lothair I. This Francia Media was partitioned by Lothair I in the year 855 between his sons: the elder, Louis II, received Italy and the imperial title; the younger, Lothair, received the northern area, henceforward known as Lothair's kingdom, or Lotharingia.
This kingdom was bounded on the north by the North Sea; on the east by a line from the mouth of the Ems River to Wesel and then by the Rhine southward to the confluence of the Aare River (but with a westward recession of the frontier that left Mainz, Worms, and Speyer to the Germans); on the south by the Aare and by the Jura Mountains; and on the west by the Saône River and the Ornain, Meuse, and Schelde rivers.
Now that we have the deed to the property straightened out, the reason for the name becomes clearer. The Séminaire Lotharingien de Combinatoire is a series of conferences in combinatorics that are held annually throughout roughly the boundaries of the ancient kingdom, which is to say, throughout, roughly, western Europe.
Very recently, because of more hard work by Dominique and with assistance from his friends, the Séminaire has evolved further. In addition to the annual conferences there is an electronic journal of the same name, which publishes the papers of the new conferences and also is in the process of reconstructing, in electronic form, the papers of past conferences from 1980 to the present.
You should be sure to have a look at that lovely web site. Instead of saying the URL here, I'll refer you to Dominique or to the link to the Séminaire journal that is in the site of the Electronic Journal of Combinatorics.
But it is very much not the case that we honor Dominique only for his creation and nurturing of the Séminaire, important as that is. It is the case that for nearly forty years - forty years - he has been a creative, prolific, and influential combinatorialist, of the first rank.
I will list a few details of those contributions, but first I must say this. At one point in time I was searching the web to find a citation to Dominique's work, so I typed in an appropriate search string, and I discovered, for instance, the following quotation:
"As soon as something pleasant and cheerful and confectionary occurs to me, I'll write about it; but I can only write about whatever comes. And what has come this far has been a kind of blackness. People say that there is no love in much of the stuff that I write. I'm not sure that it is true; I hope it's not true. I think there is love; I just don't think there is love the way most people want to use the word."
Was that a quotation from Dominique? Not at all. That quotation is from the author Harry Crews, as described in an article entitled "Interview with Harry Crews: May 1972." published in the journal Recherches Anglaises et Americaines 5 (1972): 207-225. The interviewer was a Foata, but it was not Dominique. It was his wife Anne (would you raise your hand, Anne?) who is herself a very productive writer, and whose works I encountered many times during my web meanderings. From this I gained an increased understanding of Dominique: he simply had to be productive or he would have been only number 2 in the family hierarchy very quickly. It's just a variation on the theme of "publish or perish." I'd better drop this subject now because Dominique will get a chance to rebut what I'm saying in a few minutes.
To get back to his own work, he has made, first of all, contributions to factorial design theory, enumeration of trees, Eulerian numbers, parking functions, the tangent and secant numbers, Genocchi numbers, Young tableaux, the combinatorics of orthogonal polynomials, the Robinson-Schensted correspondence, Jacobi polynomials, q-analogues, permutation statistics, combinatorics of words, the Jacobi identity and other areas too numerous to mention.
In addition, during a long and very productive collaboration with the late great Marco Schutzenberger, contributions flowed out to many more subject areas, including Eulerian polynomials, the reflection principle, exponential structures, rook polynomials, and the major index. Additional fruitful collaborations, with Volker Strehl, with Doron Zeilberger, and with others round out the picture of one of the pre-eminent combinatorialists of our time.
Dominique, welcome to the ranks of the over 65 ! We all wish you many happy, healthy and productive years to come.