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Livres
Algebraic Combinatorics and Coinvariant Spaces , CMS Treatise in Mathematics , CRC Press, 2009 . 221 pages. (voir le site web de CRC Press) (voir La table des matières et l’introduction ).
(avec P. Leroux et G. Labelle ) Combinatorial Species and Tree-like Structures , Encyclopedia of Mathematics, Cambridge University Press, 1998 . 497 pages.
(Version améliorée PDF des premiers chapitres ) (Avant-propos par Gian-Carlo Rota )
(avec P. Leroux et G. Labelle ) Théorie des espèces et combinatoire des structures arborescentes , Publications du Lacim, No. 19, UQAM, 1994 .
Certains de mes articles récents (voir mes articles sur ArXiv , sur Orcid , ou sur MathSciNet si vous y avez accès)
$(GL_k\times S_n)$-Modules of Multivariate Diagonal Harmonics , dans Open Problems in Algebraic Combinatorics, Proceedings of Symposia in Pure Mathematics, vol. 110, Amer. Math. Soc., Providence, RI, 2024, pp. 1-22. (see arXiv:2003.07402 )
Triangular Diagonal Harmonic Conjectures , Experimental Mathematics , avril 2024. arXiv:2303.02224 , 18 pages. doi.org/10.1080/10586458.2024.2336074
(avec J. Haglund , A. Iraci , and M. Romero ), The Super Nabla Operator , arXiv:2303.00560 , 54 pages. En cours de révisions.
(avec M. Mazin ) Combinatorics of Triangular Partitions , Enumerative Combinatorics and Applications , ECA 3:1 (2023 ) Article S2R1, 24 pages. (voir arXiv:2203.15942)
$(GL_k\times S_n)$-Modules and Nabla of Hook-Indexed Schur Functions , Algebraic Combinatorics , Volume 5 (2022 ) no. 5, pp. 1033-1051. (voir arXiv:1909.03531 )
The Bosonic-Fermionic Diagonal Coinvariant Modules Conjecture , arXiv:2005.00924 , 2020 , 8 pages.
(avec J.-C. Aval ) Interlaced Rectangular Parking Functions , Séminaire Lotharingien de Combinatoire , B81h (2020 ), 15 pp. (arXiv:1503.03991 ).
(avec C. Reutenauer ), Golden Ratio and Phyllotaxis, a Clear Mathematical Link? (arXiv:1704.02880 ) Journal of Mathematical Biology (2019 ). DOI: 10.1007/s00285-018-1265-3 .
(avec J.-C. Aval ) A Note on: Rectangular Schröder Parking Function Combinatorics , Séminaire Lotharingien de Combinatoire 79 (2018), Art. B79b, 2019, 13 pages. (arXiv:1603.09487 ).
Open Questions for Operators Related to Rectangular Catalan Combinatorics , Journal of Combinatorics Vol. 8, No. 4 (2017 ), pp. 673-703. (arXiv:1603.04476 ).
A $q$-Analog of Foulke’s Conjecture , Electronic Journal of Combinatorics , Volume 24, Issue 1 (2017) , Paper #P1.38 (arXiv:1602.08134 ).
Bounded Height Interlaced Pairs of Parking Functions , Discrete Mathematics , Volume 340, Issue 5 (2017) , pp. 1054-1058. (arXiv:1504.07136 ).
(avec E. Leven , A. Garsia , et G. Xin ), Compositional $(km,kn)$-Shuffle Conjectures , International Mathematics Research Notices , Vol. 2016, 4229 – 4270 doi: 10.1093/imrn/rnv272 (arXiv:1404.4616 )
(avec E. Leven , A. Garsia , et G. Xin ), Some remarkable new Plethystic Operators in the Theory of Macdonald Polynomials , Journal of Combinarorics Volume 7, Number 4, 671–714, 2016 . (arXiv: 1405.0316 )
(avec J.-C. Aval et A. M. Garsia ) Combinatorics of Labelled Parallelogram Polyominos , Journal Combinatorial Theory Series A , 132 (2015 ), 32–57 . (arXiv:1301.3035 ) MathReview .
Multivariate Diagonal Coinvariant Spaces for Complex Reflection Groups , Advances in Mathematics , 239 (2013 ), 97–108 . (arXiv:1105.4358 ) MathReview .
(avec M. Haiman ) Tableaux Formulas for Macdonald Polynomials , édition spéciale en l’honneur du $60^{e}$ anniversaire de Christophe Reutenauer, International Journal of Algebra Computations, . Volume 23 (2013 ), no. 4, 833–852. MathReview . (PDF file )
(avec L.F. Préville-Ratelle ) Higher Trivariate Diagonal Harmonics via generalized Tamari Posets , Journal of Combinatorics , 3 (2012 ), no. 3, 317–341 . (arXiv:1105.3738 ) MathReview .
(avec J.-C. Aval ) Co-quasi-invariant spaces for generalized symmetric groups , Journal of Combinatorial Theory Series A , 119 (2012 ), no. 7, 1432–1446 . (arXiv:1107.0537 )
(avec N. Borie , et N. M.Thiéry ) Deformed diagonal harmonic polynomials for complex reflection groups , FPSAC’2011, DMTCS proceedings (2011 ), 135-146. (arXiv :1011.3654 )
(avec C. Reutenauer ) $SL_k$-tilings of the plane , Illinois Journal of Mathematics , Volume 54, Number 1 (2010 ), 263-300. (arXiv :1002.1089 ). MathReview .
(avec A. Lauve ) Invariant and coinvariant spaces for the algebra of symmetric polynomials in non-commuting variables , Electronic Journal of Combinatorics , Volume 17 (2010 ), R166, 17 pages. (arXiv:0910.3024 )
(with A. M. Garsia and N. Wallach ) Harmonics for Deformed Steenrod Operators ,(FPSAC’2010), DMTCS Proceedings (2010 ) , 11 pages. (arXiv:0812.3566 ).
Certains de mes articles plus anciens
(avec J.-C. Aval et N. Bergeron ) Diagonal Temperley-Lieb Invariants and Harmonics , Séminaire Lotharingien de Combinatoire . B54Aq (2006 ), 19 pp. (hal-00185498v1 )
(avec R. Biagioli } Tensorial square of the Hyperoctahedral group Coinvariant Space , Electronic Journal of Combinatorics , (2006 ), R38.
(avec R. Biagioli et M.Rosas ) Inequalities Between Littlewood-Richardson Coefficients , Journal of Combinatorial Theory Series A , Volume 113, Issue 4, (2006 ), 567–590 . (arXiv:math/0403541 )
(avec J.-C. Aval et N. Bergeron ) Ideals of quasi-symmetric functions and super-covariant polynomials for $\mathbb{S}_n$, Advances in Mathematics, Volume 181, issue 2 (2004 ), 353–367. (arXiv:math/0202071 ) (hal-00185495v1 )
(avec 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 and N. Bergeron ) Lattice Diagram Polynomials in One Set of Variables , Special number of Advances Applied Mathematics , to the memory of Rodica Simion, Volume 28, Issues 3-4, (2002), 343-359.
(avec S. Hamel ) Intersection of Modules Related to Macdonald’s Polynomials , Discrete Mathematics, Volume 217, Issues 1-3 (2000 ), 51-64 .
(avec F. Gascon ) Counting Young Tableaux of Bounded Height , Journal of Integer Sequences , Volume 3 (2000 ), Article 00.1.7 .
(avec A. M. Garsia et G. Tesler ) Multiple Left Regular Representations Generated by Alternants , Journal of Combinatorial Theory Series A , vol. 91 (2000 ), 49–83 .
(avec N. Bergeron , A. M. Garsia , M. Haiman et G. Tesler ) Lattice Diagram Polynomials and Extended Pieri Rules , Advances in Mathematics , vol. 142 Issue 2, (1999 ), 244–334 . (arXiv:math/9809126 )
(avec A. M. Garsia , M. Haiman et G. Tesler ) Identities and Positivity Conjectures for Some Remarkable Operators in the Theory of Symmetric Functions , Methods and Applications of Analysis, Volume 6 Number 3 (1999 ), 363–420 .
(avec A. M. Garsia ) Science Fiction and Macdonald’s Polynomials , in Algebraic Methods and q -Special Functions, J.P. Van Dijen, L.Vinet (eds.), CRM Proceedings & Lecture Notes , AMS , 1999 , 1–52. (arXiv:math/9809128 )
(avec M. Bousquet-Mélou et S. Dulucq ) Standard Paths in the Composition Poset , Annales des sciences mathématiques du Québec , Volume 19, (1995 ), 139-151 .
(avec L. Favreau ), Fourier Transform for Some Semisimple Algebras and Harmonic Analysis for Probabilistic Algorithms , Discrete Math .,Volume 139, (1995 ), 19-32 .
(avec D. Krob et L. Favreau ) Conjectures on the enumeration of tableaux of bounded height, Discrete Mathematics , Elsevier, 1995, 139, pp.463-468 . (hal-00017723v1 )
(avec J. Berstel et S. Brlek ) Efficient Computation of Addition Chains , Journal de théorie des nombres de Bordeaux , vol. 6 (1994 ), 21–38 . (hal-00619346v1 )
(with N. Bergeron ) Orthogonal Idempotents in the Descent Algebra of $B_n$ and Applications , Journal of Pure and Applied Algebra, Volume 79, Issue 2 (1992 ), 109–129 .
(avec N. Bergeron , B. Howlett et D. Taylor ) A Decomposition of the Descent Algebra of Finite Coxeter Groups , Journal of Algebraic Combinatorics , Volume 1, Issue 1, (1992 ), 23–42.
(avec N. Bergeron ) A Decomposition of the Descent Algebra of the Hyperoctahedral Group , Journal of Algebra , Volume 148, Issue 1 (1992 ), 86–97 .
(avec Ph. Flajolet et B. Salvy ) Varieties of Increasing Trees , Proc. CAAP’92, Ed.: J.-C. Raoult, Lect. Notes in Comp. Sc. , No. 581, Springer-Verlag, 1992 , 24-48 . (inria-00074977v1 )
(avec S. Plouffe ) Computing the generating function of a series given its first few terms , Experimental Mathematics , Vol. 1, no. 4, (1992 ) 307-312 . (PDF )
(with A. M. Garsia and C. Reutenauer ) Homomorphisms Between Solomon’s Descent Algebras , Journal of Algebra, Volume 150, Issue 2 (1992 ), 503-519 .
(avec J. Berstel , S. Brlek et C. Duboc ) Addition Chains Using Continued Fractions , J ournal of Algorithms , Volume 10, Issue 3 (1989 ), 403–412 . (hal-00619347v1 )
Thèse
Mes diverses notes de cours
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 and G. Labelle ) Combinatorial Species and Tree-like Structures , Encyclopedia of Mathematics, Cambridge University Press, 1998 . 497 pages. (PDF of a rewriting of the First Chapters ) (Foreword by Gian-Carlo Rota )
(with P. Leroux and G. Labelle ) Théorie des espèces et combinatoire des structures arborescentes , Publications du Lacim, No. 19, UQAM, 1994 .
(with M. Mazin ) Combinatorics of Triangular Partitions , arXiv:2203.15942 , 2022, 24 pages.
The Bosonic-Fermionic Diagonal Coinvariant Modules Conjecture , Upcoming OPAC proceedings (see here ), or arXiv:2005.00924 , 2020 , 8 pages.
$(GL_k\times S_n)$-Modules of Multivariate Diagonal Harmonics , Upcoming OPAC proceedings (see here ), or arXiv:2003.07402 , 2020 . 20 pages.
$(GL_k\times S_n)$-Modules and Nabla of Hook-Indexed Schur Functions , Accepted in Algebraic Combinatorics , arXiv:1909.03531 , 2019 . 18 pages.
(with J.-C. Aval ) Interlaced Rectangular Parking Functions , Séminaire Lotharingien de Combinatoire , B81h (2020 ), 15 pp. (arXiv:1503.03991 ).
(with C. Reutenauer ), Golden Ratio and Phyllotaxis, a Clear Mathematical Link? (arXiv:1704.02880 ) Journal of Mathematical Biology (2019 ). DOI: 10.1007/s00285-018-1265-3 .
(with J.-C. Aval ) A Note on: Rectangular Schröder Parking Function Combinatorics , Séminaire Lotharingien de Combinatoire 79 (2018), Art. B79b, 2019, 13 pages. (arXiv:1603.09487 ).
Open Questions for Operators Related to Rectangular Catalan Combinatorics , Journal of Combinatorics Vol. 8, No. 4 (2017 ), pp. 673-703. (arXiv:1603.04476 ).
A $q$-Analog of Foulke’s Conjecture , Electronic Journal of Combinatorics , Volume 24, Issue 1 (2017 ) Paper #P1.38 (arXiv:1602.08134 ).
Bounded Height Interlaced Pairs of Parking Functions , Discrete Mathematics , Volume 340, Issue 5 , (2017 ), pp. 1054-1058. (arXiv:1504.07136 )
(with E. Leven , A. Garsia , and G. Xin ), Compositional $(km,kn)$-Shuffle Conjectures , International Mathematics Research Notices , Vol. 2016, 4229 – 4270 DOI: 10.1093/imrn/rnv272 (arXiv:1404.4616 ).
(with E. Leven , A. Garsia , and G. Xin ), Some remarkable new Plethystic Operators in the Theory of Macdonald Polynomial s , Journal of Combinarorics , Volume 7, Number 4, 671–714, 2016 . (arXiv: 1405.0316 )
(with J.-C. Aval and A. M. Garsia ) Combinatorics of Labelled Parallelogram Polyominos , Journal Combinatorial Theory Series A , 132 (2015 ), 32–57 . (arXiv:1301.3035 ) MathReview .
Multivariate Diagonal Coinvariant Spaces for Complex Reflection Groups , Advances in Mathematics , 239 (2013 ), 97–108 . (arXiv:1105.4358 ) MathReview .
(with M. Haiman ) Tableaux Formulas for Macdonald Polynomials , Special edition in honour of Christophe Reutenauer 60 birthday, International Journal of Algebra Computations, . Volume 23 (2013 ), no. 4, 833–852. MathReview .
(with L.F. Préville-Ratelle ) Higher Trivariate Diagonal Harmonics via generalized Tamari Posets , Journal of Combinatorics , 3 (2012 ), no. 3, 317–341 . (arXiv: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 . (arXiv:1107.0537 )
(with N. Borie , and N. M.Thiéry ) Deformed diagonal harmonic polynomials for complex reflection groups , FPSAC’2011, DMTCS proceedings (2011 ), 135-146. (arXiv :1011.3654 )
(with C. Reutenauer ) $SL_k$-tilings of the plane , Illinois Journal of Mathematics , Volume 54, Number 1 (2010 ), 263-300. (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 , Volume 17 (2010 ), R166, 17 pages. (arXiv:0910.3024 )
(with A. M. Garsia and N. Wallach ) Harmonics for Deformed Steenrod Operators ,(FPSAC’2010), DMTCS Proceedings (2010 ) , 11 pages. (arXiv:0812.3566 ).
Some of my previous papers
(with J.-C. Aval and N. Bergeron ) Diagonal Temperley-Lieb Invariants and Harmonics , Séminaire Lotharingien de Combinatoire . B54Aq (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 and M.Rosas ) Inequalities Between Littlewood-Richardson Coefficients, Journal of Combinatorial Theory Series A , vol 113 Issue 4 (2006 ), 567–590. (arXiv:math/0403541 )
(with J.-C. Aval and N. Bergeron ) Ideals of quasi-symmetric functions and super-covariant polynomials for $\mathbb{S}_n$, Advances in Mathematics , vol. 181, Issues 2 (2004 ) , 353–367. (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 and N. Bergeron ) Lattice Diagram Polynomials in One Set of Variables , Special number of Advances in Applied Mathematics , to the memory of 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, Volume 217, Issues 1-3 (2000 ), 51-64 .
(with F. Gascon ) Counting Young Tableaux of Bounded Height , Journal of Integer Sequences , Volume 3 (2000 ), Article 00.1.7 .
(with A. M. Garsia and G. Tesler ) Multiple Left Regular Representations Generated by Alternants , Journal of Combinatorial Theory Series A , vol. 91 (2000 ), 49–83 .
(with N. Bergeron , A. M. Garsia , M. Haiman and G. Tesler ) Lattice Diagram Polynomials and Extended Pieri Rules , Advances in Mathematics , vol. 142 Issue 2, (1999 ), 244–334 . (arXiv:math/9809126 )
(with A. M. Garsia , M. Haiman and G. Tesler ) Identities and Positivity Conjectures for Some Remarkable Operators in the Theory of Symmetric Functions , Methods and Applications of Analysis, Volume 6 Number 3 (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 , AMS , 1999 , 1–52. (arXiv:math/9809128 )
(with M. Bousquet-Mélou and 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 , Discrete Math.,Volume 139, (1995 ), 19-32.
(with D. Krob and L. Favreau ) Conjectures on the enumeration of tableaux of bounded height, Discrete Mathematics , Elsevier, 1995, 139, pp.463-468 . (hal-00017723v1 )
(with J. Berstel and S. Brlek ) Efficient Computation of Addition Chains , Journal de théorie des nombres de Bordeaux , vol. 6 (1994 ), 21–38 . (hal-00619346v1 )
(with N. Bergeron ) Orthogonal Idempotents in the Descent Algebra of $B_n$ and Applications , Journal of Pure and Applied Algebra, Volume 79, Issue 2 (1992 ), 109–129 .
(with N. Bergeron , B. Howlett and D. Taylor ) A Decomposition of the Descent Algebra of Finite Coxeter Groups , Journal of Algebraic Combinatorics , Volume 1, Issue 1, (1992 ), 23–42.
(with Ph. Flajolet and B. Salvy ) Varieties of Increasing Trees , Proc. CAAP’92, Ed.: J.-C. Raoult, Lect. Notes in Comp. Sc. , No. 581, Springer-Verlag, 1992 , 24-48 . (inria-00074977v1 )
(with N. Bergeron ) A Decomposition of the Descent Algebra of the Hyperoctahedral Group , Journal of Algebra , Volume 148, Issue 1 (1992 ), 86–97 .
(with S. Plouffe ) Computing the generating function of a series given its first few terms , Experimental Mathematics , Vol. 1, no. 4, (1992 ) 307-312 . (PDF )
(with A. M. Garsia and C. Reutenauer ) Homomorphisms Between Solomon’s Descent Algebras , Journal of Algebra, Volume 150, Issue 2 (1992 ), 503-519 .
(with J. Berstel , S. Brlek and C. Duboc ) Addition Chains Using Continued Fractions , J ournal of Algorithms , Volume 10, Issue 3 (1989 ), 403–412 . (hal-00619347v1 )
Thesis (in french)
Certaines notes de cours/manuscrits
Macdonald polynomials and operators and Catalan Combinatorics , 25 pages, 2022 .
Symmetric Functions and Combinatorics , 65 pages, 2018 .
Introduction à la théorie des groupes , 145 pages, 2015 .
Introduction à la combinatoire algébrique , 225 pages, 2015 .
Arithmétique et géométrie classique (avec C. Hohlweg), 162 pages, 2014 .
Calcul formel (avec Maple) , 18 pages, 2014 .
Brève Introduction à la théorie des ensembles , 37 pages, 2014 .
Mathématiques algorithmique s , 183 pages, 2017 .
Introduction à la combinatoire , 228 pages, 2010 .
La cryptographie: de l’antiquité à l’internet (avec A. Goupil), 128 pages 2006 .
Non publiés (sauf sur 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.
(avec P. McNamara ) Some positive differences of products of Schur functions , 2004 , 24 pages.