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Books
Algebraic Combinatorics and Coinvariant Spaces CMS Treatise in Mathematics , CRC Press, 2009 . 221 pages. (see the CRC Press website ) (see Table of contents and Introduction ).(with P. Leroux G. Labelle Combinatorial Species and Tree-like Structures 1998 . 497 pages. (PDF of a rewriting of the First Chapters Foreword by Gian-Carlo Rota
(with P. Leroux G. Labelle Théorie des espèces et combinatoire des structures arborescentes 1994 .
$(GL_k\times S_n)$-Modules of Multivariate Diagonal Harmonics , arXiv:2003.07402 )Triangular Diagonal Harmonic Conjectures Experimental Mathematics ,doi.org/10.1080/10586458.2024.2336074 .(see arXiv:2303.02224 )(with J. Haglund A. Iraci ,M. Romero The Super Nabla Operator arXiv:2303.00560 , 54 pages. Currently being revisited .
(with M. Mazin Combinatorics of Triangular Partitions Enumerative Combinatorics and Applications 2023 ) Article S2R1, 24 pages. (see arXiv:2203.15942)
$(GL_k\times S_n)$-Modules and Nabla of Hook-Indexed Schur Functions Algebraic Combinatorics 2022 ) no. 5, pp. 1033-1051. (see arXiv:1909.03531 )The Bosonic-Fermionic Diagonal Coinvariant Modules Conjecture arXiv:2005.00924 , 2020 , 8 pages.(with J.-C. Aval Interlaced Rectangular Parking Functions Séminaire Lotharingien de Combinatoire 2020 ), 15 pp. (see arXiv:1503.03991 ).
(with C. Reutenauer ), Golden Ratio and Phyllotaxis, a Clear Mathematical Link? Journal of Mathematical Biology (2019 ). DOI: 10.1007/s00285-018-1265-3 . (see arXiv:1704.02880 )
(with J.-C. Aval A Note on: Rectangular Schröder Parking Function Combinatorics Séminaire Lotharingien de Combinatoire 79 (2018), Art. B79b, 2019, 13 pages. (see arXiv:1603.09487 ).
Open Questions for Operators Related to Rectangular Catalan Combinatorics Journal of Combinatorics 2017 ), pp. 673-703. (see arXiv:1603.04476 ).A $q$-Analog of Foulke’s Conjecture , Electronic Journal of Combinatorics Volume 24, Issue 1 (2017 ) Paper #P1.38 (see arXiv:1602.08134 Bounded Height Interlaced Pairs of Parking Functions Discrete Mathematics Volume 340, Issue 5 , (2017 ), pp. 1054-1058. (see arXiv:1504.07136 )(with E. Leven A. Garsia G. Xin , Compositional $(km,kn)$-Shuffle Conjectures , International Mathematics Research Notices Vol. 2016, 4229 – 4270 DOI: 10.1093/imrn/rnv272arXiv:1404.4616 ).
(with E. Leven A. Garsia G. Xin , Some remarkable new Plethystic Operators in the Theory of Macdonald Polynomial sJournal of Combinarorics 2016 . (see arXiv: 1405.0316 )
(with J.-C. Aval A. M. Garsia Combinatorics of Labelled Parallelogram Polyominos Journal Combinatorial Theory Series A ,2015 ), 32–57arXiv:1301.3035 ) MathReview .
Multivariate Diagonal Coinvariant Spaces for Complex Reflection Groups Advances in Mathematics ,2013 ), 97–108arXiv:1105.4358 ) MathReview .(with M. Haiman Tableaux Formulas for Macdonald Polynomials International Journal of Algebra Computations, .Volume 23 (2013 ), no. 4, 833–852. MathReview . (PDF file
(with L.F. Préville-Ratelle Higher Trivariate Diagonal Harmonics via generalized Tamari Posets Journal of Combinatorics ,2012 ), no. 3, 317–341arXiv:1105.3738 ) MathReview .
(with J.-C. Aval Co-quasi-invariant spaces for generalized symmetric groups Journal of Combinatorial Theory Series A , 119 (2012 ), no. 7, 1432–1446(see arXiv:1107.0537 )
(with N. Borie N. M.Thiéry Deformed diagonal harmonic polynomials for complex reflection groups DMTCS 2011 ),arXiv :1011.3654 )
(with C. Reutenauer -tilings of the plane Illinois Journal of Mathematics 2010 ), 263-300. (see arXiv :0812.3566 ). MathReview .
(with A. Lauve Invariant and coinvariant spaces for the algebra of symmetric polynomials in non-commuting variables Electronic Journal of Combinatorics 2010 ), R166, 17 pages. (see arXiv:0910.3024 )
(with A. M. Garsia N. Wallach Harmonics for Deformed Steenrod Operators DMTCS 2010 )arXiv:0812.3566 ).
Some of my previous papers
(with J.-C. Aval N. Bergeron Diagonal Temperley-Lieb Invariants and Harmonics , Séminaire Lotharingien de Combinatoire 2005 ), 19 pp. (hal-00185498v1 )
(with R. Biagioli Tensorial square of the Hyperoctahedral group Coinvariant Space , Electronic Journal of Combinatorics 2006 ), R38.
(with R. Biagioli M.Rosas Inequalities Between Littlewood-Richardson Coefficients, Journal of Combinatorial Theory Series A 2006 ), 567–590. (arXiv:math/0403541 )
(with J.-C. Aval N. Bergeron Ideals of quasi-symmetric functions and super-covariant polynomials for $\mathbb{S}_n$, Advances in Mathematics 2004 )arXiv:math/0202071 ) (hal-00185495v1 )
(with F. Lamontagne Decomposition of the Diagonal Action of $\mathbb{S}_n$ on the Coinvariant Space of $\mathbb{S}_n \times \mathbb{S}_n$, Lascoux FestSchrift , Séminaire Lotharingien de Combinatoire Issue 52 , (2004 ).
(with J.-C. Aval N. Bergeron Lattice Diagram Polynomials in One Set of Variables , Special number of Advances in Applied Mathematics Rodica Simion , Volume 28, Issues 3-4, (2002 ), 343-359. (arXiv:math/0103181 )
(with S. Hamel Intersection of Modules Related to Macdonald’s Polynomials , Discrete Mathematics, 2000 ), 51-64
(with F. Gascon Counting Young Tableaux of Bounded Height , Journal of Integer Sequences 2000 ), Article 00.1.7
(with A. M. Garsia G. Tesler Multiple Left Regular Representations Generated by Alternants , Journal of Combinatorial Theory Series A 2000 ), 49–83
(with N. Bergeron A. M. Garsia M. Haiman G. Tesler Lattice Diagram Polynomials and Extended Pieri Rules , Advances in Mathematics 1999 ), 244–334arXiv:math/9809126 )
(with A. M. Garsia M. Haiman G. Tesler Identities and Positivity Conjectures for Some Remarkable Operators in the Theory of Symmetric Functions , Methods and Applications of Analysis, 1999 ), 363–420
(with A. M. Garsia Science Fiction and Macdonald’s Polynomials , in Algebraic Methods and q -Special Functions, J.P. Van Dejen, L.Vinet (eds.), CRM Proceedings & Lecture Notes 1999 , 1–52. (arXiv:math/9809128 )
(with M. Bousquet-Mélou S. Dulucq ) Standard Paths in the Composition Poset , Annales des sciences mathématiques du Québec , Volume 19, (1995 ), 139-151
(with L. Favreau Fourier Transform for Some Semisimple Algebras and Harmonic Analysis for Probabilistic Algorithms , 1995 ), 19-32.
(with D. Krob L. Favreau Conjectures on the enumeration of tableaux of bounded height, Discrete Mathematics , Elsevier, 1995, 139, pp.463-468hal-00017723v1 )
(with J. Berstel S. Brlek Efficient Computation of Addition Chains , Journal de théorie des nombres de Bordeaux 1994 ), 21–38hal-00619346v1 )
(with N. Bergeron Orthogonal Idempotents in the Descent Algebra of $B_n$ and Applications , Journal of Pure and Applied Algebra, 1992 ), 109–129
(with N. Bergeron B. Howlett D. Taylor A Decomposition of the Descent Algebra of Finite Coxeter Groups , Journal of Algebraic Combinatorics 1992 ), 23–42.
(with Ph. Flajolet B. Salvy Varieties of Increasing Trees , Proc. CAAP’92, Ed.: J.-C. Raoult, Lect. Notes in Comp. Sc. 1992 , 24-48inria-00074977v1 )
(with N. Bergeron A Decomposition of the Descent Algebra of the Hyperoctahedral Group , Journal of Algebra 1992 ), 86–97
(with S. Plouffe Computing the generating function of a series given its first few terms Experimental Mathematics 1992 ) 307-312PDF )
(with A. M. Garsia C. Reutenauer Homomorphisms Between Solomon’s Descent Algebras , Journal of Algebra, 1992 ), 503-519
(with J. Berstel , S. Brlek C. Duboc Addition Chains Using Continued Fractions , J ournal of Algorithms 1989 ), 403–412hal-00619347v1 )
Thesis (in french)
My various notes (most are in french)
Macdonald polynomials and operators and Catalan Combinatorics 2022 .Symmetric Functions and Rectangular Catalan Combinatorics 2018 . Available as Open Math Notes of the AMS.Introduction à la théorie des groupes 2015 .Introduction à la combinatoire algébrique 2015 .Arithmétique et géométrie classique 2014 .Calcul formel (avec Maple) ,2014 .Brève Introduction à la théorie des ensembles 2014 .Mathématiques algorithmique s 183 pages, 2017 .Introduction à la combinatoire 2010 .La cryptographie: de l’antiquité à l’internet 2006 .
Unpublished (except on ArXiv)
A Survey of $q$-Whittaker Polynomials arXiv:2006.12591 , 2020 , 29 pages.Survey: Combinatorics of $r$ -Dyck paths, $r$ -Parking functions, and the $r$ -Tamari lattices 2012 , 36 pages.Combinatorial Cellular Decompositions for the Space of Complex Coefficient Polynomials 2011 , 22 pages.New Formulas and Conjectures for the Nabla Operator 2011 , 13 pages.(with P. McNamara Some positive differences of products of Schur functions 2004 , 24 pages.
