Dominique Foata, Doron Zeilberger
Abstract. Further computations are made on the traditional coupon collector’s problem when the collector shares his harvest with his younger brothers. When the book of the p-th brother of the...
Babson-Steingrímsson statistics are indeed Mahonian (and sometimes even Euler-Mahonian (2009)
Dominique Foata, Doron Zeilberger
Babson and Steingrímsson have recently introduced seven new permutation statistics, that they conjectured were all Mahonian (i.e., equi-distributed with the number of inversions). We prove their...
Signed words and permutations, II; The Euler-Mahonian polynomials (2009)
Dans la théorie de Morse, quand on veut étudier un espace, on introduit une fonction numérique; puis on aplatit cet espace sur l’axe de la valeur de cette fonction. Dans cette opération...
RANDOM PERMUTATIONS AND BERNOULLI SEQUENCES (2009)
ABSTRACT. — The so-called first fundamental transformation provides a natural combinatorial link between statistics involving cycle lengths of random permutations and statistics dealing with runs...
New permutation coding and equidistribution of set-valued statistics (2009)
Foata, Dominique, Han, Guo-Niu
A new coding for permutations is explicitly constructed and its association with the classical Lehmer coding provides a bijection of the symmetric group onto itself serving to show that six...
New permutation coding and equidistribution of set-valued statistics (2009)
Foata, Dominique, Han, Guo-Niu
A new coding for permutations is explicitly constructed and its association with the classical Lehmer coding provides a bijection of the symmetric group onto itself serving to show that six...
The collector's brotherhood problem using the Newman-Shepp symbolic method (2008)
Dominique Foata, Doron Zeilberger
Abstract. Further computations are made on the traditional coupon collector’s problem when the collector shares his harvest with his younger brothers. When the book of the p-th brother of the...
Babson-Steingrímsson statistics are indeed Mahonian (and sometimes even Euler-Mahonian (2008)
Dominique Foata, Doron Zeilberger
Abstract: Babson and Steingrímsson have recently introduced seven new permutation statistics, that they conjectured were all Mahonian (i.e. equi-distributed with the number of inversions). We prove...
ABSTRACT. The generating function for words by a multivariable statistic involving decrease, increase, descent and rise values is explicitly calculated by using the MacMahon Master Theorem and the...
Signed words and permutations, IV; Fixed and pixed points (2008)
und Lust zu diskretieren.
2007/05/23 A four-variable distribution on permutations is derived, with two dual combinatorial interpretations. The first one includes the number of fixed points “fix”, the second the so-called...
Dominique Foata, Guo-niu Han, Glory To Viennot, Only Verbatim
No one can beat him.
Signed words and permutations, II; The Euler-Mahonian polynomials (2008)
Dans la théorie de Morse, quand on veut étudier un espace, on introduit une fonction numérique; puis on aplatit cet espace sur l’axe de la valeur de cette fonction. Dans cette opération...
Dominique Foata, Guo-niu Han, Glory To Viennot, Only Verbatim
No one can beat him.
The Lotharingian impact on Combinatorial Mathematics: myth or reality? (2008)
Dominique Foata, Dominique Foata
It is very fortunate that two, and sometimes three, sessions of the Séminaire Lotharingien have been held every year since its beginning in 1980. Otherwise, several of us, at least the confirmed...
Running head is “TRANSFORMATIONS ON WORDS” Proofs should be sent to (2008)
Dominique Foata, Guo-niu Han, Guo-niu Han
The purpose of this paper is to give the description of a single algorithm that specializes into several classical transformations derived on words, namely the Cartier-Foata transform, its contextual...
Two oiseau decompositions of permutations and their application to Eulerian calculus (2008)
Abstract: Two transformations are constructed that map the permutation group onto a well-defined subset of a partially commutative monoid generated by the so-called oiseaux. Those transformations are...
ABSTRACT. The generating function for words by a multivariable statistic involving decrease, increase, descent and rise values is explicitly calculated by using the MacMahon Master Theorem and the...
Une méthode combinatoire pour l’étude des fonctions spéciales (2007)
Foata, Dominique; Institut Lothaire, 1 Rue Murner 67000 Strasbourg,
La méthode du composé partitionnel, introduite en mathématiques combinatoires dans les années soixante-dix, a permis d'établir de nombreuses identités classiques sur les fonctions spéciales....
Dominique Foata, Doron Zeilberger, To Marco Schutzenberger, In Memoriam
classic proof of a recurrence
Universit'e Louis Pasteur, Strasbourg (2007)
The purpose of this talk is to study the behaviour of several classical statistics on words, such as the number of descents, the number of excedances, the major index, when the strict inequalities
Combinatorial Proofs Of Capelli's And Turnbull's Identities From Classical Invariant Theory (2007)
Dominique Foata, Doron Zeilberger
this paper, we give short combinatorial proofs of Capelli's and Turnbull's identities, and raise the hope that someone else will use our approach to prove the new Howe-Umeda-Kostant-Sahi...
Combinatorial Proofs Of Capelli's And Turnbull's Identities From Classical Invariant Theory (2007)
Dominique Foata, Doron Zeilberger
this paper, we give short combinatorial proofs of Capelli's and Turnbull's identities, and raise the hope that someone else will use our approach to prove the new Howe-Umeda-Kostant-Sahi...
Word straightening and q-Eulerian Calculus (2007)
. This paper contains a new description of the straightening algorithm for pairs of finite words called circuits. The commutation rule underlying the straightening algorithm that keeps invariant a...
Eulerian Calculus: a Technology for Computer Algebra and Combinatorics (2007)
Summary by Dominique Gouyou-Beauchamps Babson and Steingrmsson have introduced pairs of permutation statistics that they conjectured were all Euler{Mahonian, i.e., equidistributed with the pair (des;...
Doron Zeilberger, David Bressoud, Gaurav Bhatnagar, Anders Bjorner, Jonathan Borwein, Francesco Brenti, ...
Two stones build two houses. Three build six houses. Four build four and twenty houses. Five build hundred and twenty houses. Six build Seven hundreds and twenty houses. Seven build five thousands...
Http Algo Inria, Dominique Foata, Summary Cyril Banderier
The classical coupon-collector problem is here extended to the case where the collector shares his harvest with other members of his phratry. She (!) remains the single buyer, but she gives to his...
Une méthode combinatoire pour l’étude des fonctions spéciales (2007)
La méthode du composé partitionnel, introduite en mathématiques combinatoires dans les années soixante-dix, a permis d'établir de nombreuses identités classiques sur les fonctions spéciales....
Fix-Mahonian Calculus III; a Quadruple Distribution (2007)
Foata, Dominique, Han, Guo-Niu
A four-variable distribution on permutations is derived, with two dual combinatorial interpretations. The first one includes the number of fixed points "fix", the second the so-called "pix"...
Fix-Mahonian Calculus, II: further statistics (2007)
Foata, Dominique, Han, Guo-Niu
Using classical transformations on the symmetric group and two transformations constructed in Fix-Mahonian Calculus I, we show that several multivariable statistics are equidistributed either with...
Fix-Mahonian Calculus, I: two transformations (2007)
Foata, Dominique, Han, Guo-Niu
We construct two bijections of the symmetric group S_n onto itself that enable us to show that three new three-variable statistics are equidistributed with classical statistics involving the number...
Signed words and permutations, IV; Fixed and pixed points (2007)
Foata, Dominique, Han, Guo-Niu
The flag-major index "fmaj" and the classical length function "$\ell$" are used to construct two $q$-analogs of the generating polynomial for the hyperoctahedral group~$B_n$ by number of positive and...
Specializations and Extensions of the quantum MacMahon Master Theorem (2007)
Foata, Dominique, Han, Guo-Niu
We study some specializations and extensions of the quantum version of the MacMahon Master Theorem derived by Garoufalidis, Le and Zeilberger. In particular, we obtain a (t,q)-analogue for the...
A basis for the right quantum algebra and the "1=q" principle (2007)
Foata, Dominique, Han, Guo-Niu
We construct a basis for the right quantum algebra introduced by Garoufalidis, Le and Zeilberger and give a method making it possible to go from an algebra submitted to commutation relations (without...
Fix-Mahonian Calculus, I: two transformations (2007)
Foata, Dominique, Han, Guo-Niu
We construct two bijections of the symmetric group S_n onto itself that enable us to show that three new three-variable statistics are equidistributed with classical statistics involving the number...
Fix-Mahonian Calculus, II: further statistics (2007)
Foata, Dominique, Han, Guo-Niu
Using classical transformations on the symmetric group and two transformations constructed in Fix-Mahonian Calculus I, we show that several multivariable statistics are equidistributed either with...
A Complement, Guo-niu Han, Guoce Xin, Dominique Foata
a fundamental transformation, Proc. Amer. Math. Soc., vol. 135, 2007, no. 1, 31-40.- 15-
Signed words and permutations, IV; Fixed and pixed points (2006)
Foata, Dominique, Han, Guo-Niu
The flag-major index "fmaj" and the classical length function "$\ell$" are used to construct two $q$-analogs of the generating polynomial for the hyperoctahedral group~$B_n$ by number of positive and...
A basis for the right quantum algebra and the "1=q" principle (2006)
Foata, Dominique, Han, Guo-Niu
We construct a basis for the right quantum algebra introduced by Garoufalidis, Le and Zeilberger and give a method making it possible to go from an algebra submitted to commutation relations (without...
A New Proof of the Garoufalidis-Le-Zeilberger Quantum MacMahon Master Theorem (2006)
Foata, Dominique, Han, Guo-Niu
We propose a new proof of the quantum version of MacMahon's Master Theorem, established by Garoufalidis, Le and Zeilberger.
Specializations and Extensions of the quantum MacMahon Master Theorem (2006)
Foata, Dominique, Han, Guo-Niu
We study some specializations and extensions of the quantum version of the MacMahon Master Theorem derived by Garoufalidis, Le and Zeilberger. In particular, we obtain a (t,q)-analogue for the...
Signed Words and Permutations, I; a Fundamental Transformation (2006)
This paper is dedicated to the memory of Percy Alexander MacMahon Abstract. The statistics major index and inversion number, usually defined on ordinary words, have their counterparts in signed...
Fix-Mahonian Calculus, I: two transformations, arXiv (2006)
on the occasion of the LerouxFest. ABSTRACT. We construct two bijections of the symmetric group Sn onto itself that enable us to show that three new three-variable statistics are equidistributed with...
Specializations and Extensions of the quantum MacMahon Master Theorem (2006)
ABSTRACT. We study some specializations and extensions of the quantum version of the MacMahon Master Theorem derived by Garoufalidis, Lê and Zeilberger. In particular, we obtain a (t, q)-analogue...
A New Proof of the Garoufalidis-Lê-Zeilberger Quantum MacMahon Master Theorem (2006)
ABSTRACT. We propose a new proof of the quantum version of MacMahon’s Master Theorem, established by Garoufalidis, Lê and Zeilberger. RÉSUMÉ. Nous proposons une nouvelle démonstration de la...
Fix-Mahonian Calculus, II: further statistics (2006)
ABSTRACT. Using classical transformations on the symmetric group and two transformations constructed in Fix-Mahonian Calculus I, we show that several multivariable statistics are equidistributed...
Signed Words and Permutations, I; a Fundamental Transformation (2006)
This paper is dedicated to the memory of Percy Alexander MacMahon. Abstract. The statistics major index and inversion number, usually defined on ordinary words, have their counterparts in signed...
Th\'eorie G\'eom\'etrique des Polyn\^omes Eul\'eriens (2005)
Foata, Dominique, Schützenberger, Marcel-Paul
This is the classical monograph on the combinatorial study of Eulerian polynomials, published in 1970. It has been retyped in TeX and made available on the web with the kind permission of...
A basis for the right quantum algebra and the “1 = q” principle (2005)
Abstract. We construct a basis for the right quantum algebra introduced by Garoufalidis, Lê and Zeilberger and give a method making it possible to go from an algebra subject to commutation relations...
PERMUTATION STATISTICS (Preliminary version) (2004)
Dominique Foata, Dominique Foata, Guo-niu Han, Guo-niu Han, Pasteur Cnrs
1. The q-binomial theorem
A combinatorial proof of Bass’s evaluations of the Ihara-Selberg zeta function for graphs (1999)
Dominique Foata, Doron Zeilberger
This paper is dedicated to Gian-Carlo Rota, on his millionth2’s birthday. Abstract. We derive combinatorial proofs of the main two evaluations of the Ihara-Selberg zeta function associated with a...
The Triple, Quintuple And Septuple Product Identities Revisited (1999)
. This paper takes up again the study of the Jacobi triple and Watson quintuple identities that have been derived combinatorially in several manners in the classical literature. It also contains a...
A Combinatorial Proof of Bass's Evaluations of the Ihara-Selberg Zeta Function for Graphs (1998)
Foata, Dominique, Zeilberger, Doron
We derive combinatorial proofs of the main two evaluations of the Ihara-Selberg Zeta function associated with a graph. We give three proofs of the first evaluation all based on the algebra of Lyndon...
A Classic Proof of a Recurrence for a Very Classical Sequence (1998)
Foata, Dominique, Zeilberger, Doron
By practicing the philosophy of our beloved late master, Marco Schutzenberger, to whose memory this article is dedicated, we give an insightful bijective proof of the three-term recurrence satisfied...
. The inverse of a permutation is one of the basic operations in the symmetric group. In this paper we propose an extension of this operation to words (with repetitions) by constructing an explicit...
Transformations on Words and q-Calculus (1998)
Contents 10 Transformations on Words and q-Calculus 1 10.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 10.1 The q-binomial coefficients . . . . . . . . . . . . . . . . ....
Transformations On Words (1997)
Guo-niu Han, Guo-niu Han, Dominique Foata, Dominique Foata, Dominique Foata, Guoniu Han, ...
The purpose of this paper is to give the description of a single algorithm that specializes into several classical transformations derived on words, namely the Cartier-Foata transform, its contextual...
Dominique Foata, Doron Zeilberger, Communicated George Andrews
to marco schutzenberger, in memoriam Richard Stanley [St96] has recently narrated the fascinating story of how the classical Schroder [Sch1870] numbers s(n) are even more classical than was...
Toulouse, Mathilde., Foata, Dominique.
Tese (Doutorado)--Université Louis Pasteur, 25/11/1996.
Graphical major indices (1995)
Dominique Foata, Doron Zeilberger
Abstract: A generalization of the classical statistics "maj " and "inv " (the major index and number of inversions) on words is introduced, parameterized by...
Graphical major indices (1995)
Dominique Foata, Doron Zeilberger
Abstract: A generalization of the classical statistics "maj " and "inv " (the major index and number of inversions) on words is introduced, parameterized by...
Proof Of The Alternating Sign Matrix Conjecture (1995)
Doron Zeilberger, Gert Almkvist, Noga Alon, George Andrews, Dror Bar-natan, Francois Bergeron, ...
: The number of n n matrices whose entries are either -1, 0, or 1, whose row- and column- sums are all 1, and such that in every row and every column the non-zero entries alternate in sign, is proved...
The Graphical Major Index (1994)
Foata, Dominique, Zeilberger, Doron
A generalization of the classical statistics ``maj'' and ``inv'' (the major index and number of inversions) on words is introduced, parameterized by arbitrary graphs on the underlying alphabet. The...
Eulerian Calculus, IV: Specializations (1994)
Robert J. Clarke, Dominique Foata
. --- Further excedance and descent statistics can be defined on each rearragement class and their generating functions explicitly calculated. Those generating functions coincide with the classical...
Combinatorial Proofs of Capelli's and Turnbull's Identities from Classical Invariant Theory (1993)
Foata, Dominique, Zeilberger, Doron
Capelli's and Turnbull's classical identities are given elegant combinatorial proofs.
Laguerre polynomials, weighted derangements, and positivity (1988)
Dominique Foata, Doron Zeilberger:i
Abstract. A calculation of the linearization coefficients of the (generalized) Laguerre polynomials L")(x) is proposed by means of analytic and combinatorial methods. This paper extends to the...
Linearization Coefficients For The Jacobi Polynomials (1987)
Dominique Foata, Doron Zeilberger
. --- The explicit non-negative representation of the linearization coefficients of the Jacobi polynomials obtained by RAHMAN seems to be difficult to be derived by combinatorial methods. However...
Linearization coefficients for the Jacobi polynomials (1987)
Dominique Foata, Doron Zeilberger
RÉSUMÉ. — Une formule explicite pour les coefficients de linéarisation des polynômes de Jacobi a été donnée par RAHMAN, d’où l’on tire, sans calcul, les propriétés de positivité....
Weighted Derangements And Laguerre Polynomials (1984)
Dominique Foata, Doron Zeilberger
this paper to provide one by taking up again the combinatorial model introduced by GILLIS and EVEN [7] and "ff-extending" it. Let P(n 1 ; : : : ; nm ) be the set of permutations on the n 1...
Weighted derangements and Laguerre polynomials (1984)
Dominique Foata, Doron Zeilberger
of the theory of special functions was a remarkable result of GILLIS and EVEN [7] that gave a certain combinatorial interpretation to the linearization coefficients of the simple Laguerre polynomials...
Foata, Dominique, Schutzenberger, Marcel P
Incluye bibliografía
Thesis (doctoral)--Faculté des sciences de Paris, 1965.
Jacobi And Watson Identities Combinatorially Revisited
. This paper takes up again the study of the Jacobi and Watson identities that have been derived combinatorially in several manners in the classical literature. 1. Introduction In the classical...
Jacobi And Watson Identities Combinatorially Revisited
this paper is to give combinatorial proofs of both identities (1) and (2) that use the same geometrical set-up based on the traditional Ferrers diagrammes used for partitions. The quintuple product...