Classical Combinatorics

In honor of Dominique Foata's 65th birthday

Temple University
1616 Walnut Street, Philadelphia, PA
July 7-9, 2000

Participants | Dominique's Doctorate Directions | Expense Report Info | Poster | Schedule of Speakers


At the Banquet

The banquet was truly a wonderful celebration of Dominique's accomplishments. Below is Herb Wilf's speech, along with Dominique's rebuttle.

Herb Wilf

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. However, there are some similarities, so I would like to begin by saying just a couple of the same things I said to Paul Bateman, at the risk of boring a few of you who also attended the Illinois conference. Let me offer a few pieces of wisdom and advice for you to think about as the years go by.

First, Forget about the past -- because you can't change it. Forget about the future -- because you can't predict it. And forget about the present because I didn't get you one.

Next, always remember what W C Fields said: Start every day with a smile --- and get it over with.

Also, Dominique, Don't worry about avoiding temptation; at your age temptation will start avoiding you.

And soon, when you first turn on your computer, it will tell you that you need an upgrade.

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 Seminaire 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 Seminaire? 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 toCharles 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 Sa=F4ne 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 Seminaire 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 S=E9minaire 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 Seminaire 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 S=E9minaire, 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.


A reply to Herb Wilf

How can I compete with Herb's brilliant art of public speaking? All he said is beyond truth. For sure, I do not deserve all these wonderful niceties. Let me thank him on behalf of all of you, so that the burden of those niceties will be easier to carry.

It is fortunate (or unfortunate) that I have just completed reading Umberto Eco's essay, entitled ``How to travel with a salmon". His chapter ``How to Write an Introduction", where he explains how to write a chapter of thanks ``in accordance with the rules long established in the academic world" would have made the ideal speech. But each discourse is to remain personal. I will then only quote him on one occasion.

The first time I heard of the so-called FoataFest was in Strasbourg in the Spring of 1999. Guoniu Han came to my office and explained that he had received an email from Doron, urging him to make plans for a mathematical conference on the occasion of my 65th birthday. Guoniu was awfully embarrassed. ``Don't worry," I said, ``simply write back that you don't feel at ease being in charge of such meetings, that you have just helped the others do so. He will perfectly understand." I thought that I was safe and the question was settled once for all.

On the contrary, when I visited Doron last Summer, he was more resolute than ever, and asked me permission to have such a meeting at Temple. My answer was: yes, if it be an excuse for having a friendly gathering of the very many dear friends and colleagues we have in America. Then he started right away sending letters of invitation to all of you, superbly assisted by the young Aaron who brought his internet skills to the project. So, here we are, gathered in the heart of historical America.

America, I have a great indebtedness to this country. It has brought me so much in my career, has allowed me to meet with great masters, Henry B. Mann, who died a few months ago at the age of 95, a Viennese \'emigr\'e, a number theorist, but also a great combinatorialist and statistician, Raj-Chandhra Bose, who disproved the Euler conjecture on orthogonal Latin Squares, John Riordan, who wrote the first book on Combinatorics in modern times and had also been a gifted short story writer, and more recently, with several others such as Dick Askey, George Andrews, Doron Zeilberger, Herb Wilf, but I shall come back to them in a moment.

Let me mention the names of the dear friends who have left us, Rodica Simion (I am reading her great survey paper on Enumerative Combinatorics that has just appeared in Discrete Mathematics; I admire her great mathematical elegance). Gian-Carlo Rota could have been here too. I thank Richard Stanley for the beautiful texts he wrote about him and his works. May I mention the name of Marco Sch\"utzenberger gone four years ago to whom my debt is infinite.

This meeting is having a great success, notably due to the talented young generation. May I thank all of them for having brought their significant contributions to this rencontre. I hope that they will excuse me if I focus my speech to celebrating the other young people, those people I have known for a longer time.

Doron Zeilberger, everybody knows his mathematical talent, his creativity, his leadership. Working with him is always a fantastic experience. We never expect the next idea he will develop. His works on Computer Algebraic Combinatorics (a subject that is to be added in the Mathematical Reviews Classification) have paved the way to a new approach to mathematics. Marco Sch\"utzenberger regarded his seminal paper on the subject as one of the key papers in the twentieth century. A great mathematician, for sure, but as everybody can see, a great scientific administrator, too, as he has made arrangements for this meeting so successfully. What will be his next achievement?

Aaron Robertson, what a great debut in conference making! Our profession is multifold: teaching, research, scientific advising, editorial working, conference managing. He has already brought a brilliant contribution to several of those activities. He is starting a career; the odds are favorable, I wish him the best in his promising future.

In the list of the organizers I've found the name of George Andrews. What a delight. I have known George for 28 years. He was kind enough to invite me to Penn State in 1972. At that time he was collecting the papers by MacMahon and pretended that he needed my expertise. In 1972 State College was not the metropolis it has become, it was a peaceful place in the shadow of a huge football stadium, unexpectedly populated by brilliant scholars, such as the late Chowla, and the young George. I felt like going to the court of Count Esterhazy, meeting the prestigious Josef Haydn who was writing the scores of his partitions, opus 1, opus 2, opus 3, ... , on the theme of Ramanujan and Rogers. Twenty eight years later he has become the unsurpassable q-guru in Doron's idioglottic language.

Dick Askey, known as the pope of Special Functions, has certainly educated a generation of combinatorialists in his discipline. In the mid seventies the study of Special Functions had not entered the field of Combinatorics in full force. We had timid combinatorial evaluations in terms of integrals of orthogonal polynomials, but nothing systematic had been made. I discussed the matter with George Andrews during the Berlin meeting in 1976 and asked him if he could help me have enough specialists in Special Functions for the next Oberwolfach seminar. His answer was: ``you've got to write to Dick Askey", which I did. A few days later I received a very encouraging letter from Dick in his inimitable imperial style: ``you must invite Joe Gillis (a wonderful mathematician, Doron's mentor; with some nostalgia I remember the 1986 Weizmann Institute meeting in his honor), and Chuck Dunkl, and Tom Koornwinder, and Mourad Ismail, and others. Practically all came and it was a very fascinating rencontre. I must say that the ``tableau d'Askey" or the ``Askey scheme" was born there. I was sitting next to Curtis Greene and we both were fascinated by that surprising diagramme of polynomials knowledgeably commented by his creator. Since then, Dick has remained the great scholar who has extended his influence to several fields of mathematics, including Combinatorics.

I owe a debt to Herb Wilf, I could not come to the celebration of his own 65th birthday, already in Philadelphia. Still I wanted to tell him how much I had admired his mathematical leadership. He has been the successful advisor of very many talented Penn Ph.D's. An old-timer, yes indeed. He attended the Rome conference in 1973 ``sulle Combinatorie teorie" where he met Marco Sch\"utzenberger. I remember that Marco was eager to bring a solution to a problem proposed by him. At first, Herb was annoyed by Marco's unorthodox style, but soon they became good friends. We were fortunate to have him as a main speaker at our last S\'eminaire Lotharingien in Alsace last March.

I should like to thank other participants for their highly valuable contributions, of course, the ever-lastingly young Adriano Garsia, whose mathematical enthusiasm has remained intact, Jeff Remmel, who masters both Logic and Combinatorics, Michelle Wachs, whose intellectual ability has always impressed Adriano and many others, Richard Stanley, who has become the great M.I.T. scholar, at the head of a brilliant combinatorial school, Don Richards, who has revolutionized the multivariable q-calculus, Xavier Viennot, the spirited leader of the Bordeaux school, Ira Gessel, the founder of q-calculus in combinatorics, Dennis Stanton, whose Special Functions expertise does marvels in our field, Volker Strehl, who adds the computing trick to all he touches, Pierre Leroux, the founder of the Quebec combinatorial school, Curtis Greene, whose poset Weltanschaung gives him the keenest comprehension of the algebra of Young tableaux, David Bressoud, who successfully made accessible the latest combinatorial gems to a larger audience, Rodney Canfield, who knows how to crack the hard nut of any asymptotic expression, Frank Garvan, the partition computer wizard, Christian Krattenthaler, the rising star, and many others. Please, accept my apologies for not being able to thank everybody personally.

Let me mention the names of the Strasbourg offspring, who are attending the conference: Laurent Habsieger, Jiang Zeng and Guoniu Han. I have greatly benefited from their mathematical talents. I have always wondered who the master was and who the pupil.

As a conclusion, I should like to borrow one sentence from Umberto Eco, though slightly modified, a sentence probably inspired by the Ecclesiastes: the little I have accomplished ``would not have been possible without the unfailing assistance of my wife, Anne, who, with her immeasurable and incredible literary talent, has always assured me that all is vanity."

--Dominique Foata