Page personnelle de Loïc Foissy

 

 

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Publications

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Enseignement

 

Thèse de doctorat :

·       Les algèbres de Hopf des arbres enracinés décorées. Pdf.

Habilitation à diriger des recherches :

·       Algèbres de Hopf combinatoires. Pdf.

Livre :

·       Algèbre et Calcul Formel Agrégation de Mathématiques Option C. En collaboration avec Alain Ninet. Ellipses, 2017.

Publications et preprints :

·       Surjections and double posets. En collaboration avec Frédéric Patras. Pdf, arXiv.

·       Cocommutative Com-PreLie bialgebras. Pdf, arXiv.

·       Cofree Com-PreLie algebras. Pdf, arXiv.

·       Extension of the product of a post-Lie algebra and application to the SISO feedback transformation group. Pdf, arXiv.

·       Algebraic structures associated to operads. Pdf, arXiv.

·       A theory of pictures for quasi-posets, en collaboration avec Claudia Malvenuto et Frédéric Patras. J. Algebra 477, 496-515 (2017). Pdf, arXiv, MathSciNet.

·       Chromatic polynomials and bialgebras of graphs. Pdf, arXiv.

·       Commutative and non-commutative bialgebras of quasi-posets and applications to Ehrhart polynomials. Pdf, arXiv.

·       Lie theory for quasi-shuffle bialgebras. En collaboration avec Frédéric Patras. Pdf, arXiv.

·       Operads of finite posets. En collaboration avec Frédéric Fauvet et Dominique Manchon. Pdf, arXiv.

·       Multigraded Dyson-Schwinger systems. Pdf, arXiv.

·       A divisibility result on combinatorics of generalized braids, en collaboration avec Jean Fromentin. J. Combin. Theory Ser. A 152, 190-224 (2017). Pdf, arXiv, MathSciNet.

·       The Hopf algebra of finite topologies and mould composition, en collaboration avec Frédéric Fauvet et Dominique Manchon. Ann. Inst. Fourier (Grenoble) 67 no. 3, 911-945 (2017). Pdf, arXiv, MathSciNet.

·       Deformations of shuffles and quasi-shuffles, en collaboration avec Frédéric Patras et Jean-Yves Thibon. Ann. Inst. Fourier (Grenoble) 66 no.1, 209-237 (2016). Pdf, arXiv, MathSciNet.

·       Infinitesimal and B_infinity-algebras, finite spaces, and quasi-symmetric functions, en collaboration avec Claudia Malvenuto et Frédéric Patras. J. Pure Appl. Algebra 220 no. 6, 2434-2458 (2016). Pdf, arXiv, MathSciNet.

·       Free quadri-algebras and dual quadri-algebras. Pdf, arXiv.

·       A pre-Lie algebra associated to a linear endomorphism and related algebraic structures. Eur. J. Math. 1, no. 1, 78–121 (2015). Pdf, arXiv.

·       The Hopf algebra of Fliess operators and its dual pre-Lie algebra. Comm. Algebra 43, no. 10, 4528–4552 (2015). Pdf, arXiv.

·       Examples of Com-PreLie Hopf algebras. Pdf, arXiv.

·       The Hopf algebra of finite topologies and T-partitions, en collaboration avec Claudia Malvenuto. J. Algebra 438, 130–169.Pdf, arXiv.

·       A combinatorial non-commutative Hopf algebra of graphs, en collaboration avec Gérard Duchamp, Nguyen Hoang-Nghia, Dominique Manchon et Adrian Tanasa. Discrete Math. Theor. Comput. Sci. 16, no. 1, 355-370 (2014). Pdf, arXiv.

·       Bruhat order on plane posets and applications. J. Combin. Theory Ser. A. 126, 1-23 (2014). Pdf, arXiv.

·       General Dyson-Schwinger equations and systems. Comm. Math. Phys. 327 no. 1, 151-179 (2014). Pdf, arXiv, MathSciNet.

·       Deformation of the Hopf algebra of plane posets. European J. Combin. 38, 36-40 (2014). Pdf, arXiv, MathSciNet.

·       Natural endomorphisms of shuffle algebras, en collaboration avec Frédéric Patras. Int. J. Algebra and Computation 23, no. 4 (2013) 989–1009. Pdf, arXiv, MathSciNet.

·       Pre-Lie algebras and systems of Dyson-Schwinger equations, Proceedings of the DSFdB2011 Meeting, Strasbourg. Pdf, MathSciNet.

·       Ordered forests, permutations and iterated integrals, en collaboration avec Jérémie Unterberger. Int. Math. Res. Notices, no. 4, 846-885 (2013).Pdf, arXiv, MathSciNet.

·       Plane posets, special posets and permutations. Adv.Math. 240, 24-60 (2013). Pdf, arXiv, MathSciNet.

·       Algebraic structures on double and plane posets. Journal of Algebraic Combinatorics 37 (2013), no. 1, 39-66. Pdf, arXiv, MathSciNet.

·       Ordered forests and parking functions. International Mathematics Research Notices 7, 1603-1633 (2012). Pdf, arXiv, MathSciNet.

·       Free and cofree Hopf algebras. J. Pure App. Algebra 216 (2012), no. 2, 480-494. Pdf, arXiv, MathSciNet.

·       Polynomial realization of some combinatorial Hopf algebras, en collaboration avec Jean-Christophe Novelli et Jean-Yves Thibon. Journal of Noncommutative Geometry (2012). Pdf, arXiv, MathSciNet.

·       Primitive elements of the Hopf algebra of free quasi-symmetric functions. Combinatorics and Physics, Contemp. Math. 539 (2011), 79-88. Pdf, MathSciNet.

·       Lie algebra associated to systems of Dyson-Schwinger equations. Adv. Math.226 (2011), no. 6, 4702-4730. Pdf, arXiv, MathSciNet.

·       Systems of Dyson-Schwinger equations. Pdf, arXiv.

·       Hopf subalgebras of the Hopf algebra of rooted trees coming from Dyson-Schwinger equations and Faà di Bruno Lie algebras. Motives, QFT and PsDO, Clay Math. Proc. 12 (2010), 189-210. Pdf, MathSciNet.

·       Classification of systems of Dyson-Schwinger equations in the Hopf algebra of decorated rooted trees. Adv. Math. 224 (2010), 2094-2150. Pdf, arXiv, MathSciNet.

·       The operads of planar forest are Koszul. Pdf, arXiv.

·       The infinitesimal Hopf algebra and the operads of planar forests. International Mathematics Research Notices (2009), no. 3, 395-435. Pdf, arXiv, MathSciNet.

·       Left ideals in an enveloping algebra, prelie products and applications to simple complex Lie algebras. Pdf, arXiv.

·       Free brace algebras are free prelie algebras. Comm. Algebra 38 (2010), no. 9, 3358-3369. Pdf, arXiv, MathSciNet.

·       The infinitesimal Hopf algebra and the poset of planar forests. Journal of Algebraic Combinatorics 30 (2009), 277-309. Pdf, arXiv MathSciNet.

·       An introduction to Hopf algebras of trees. Pdf.

·       Faà di Bruno subalgebras of the Hopf algebra of planar trees from combinatorial Dyson-Schwinger equations. Adv. Math. 218 (2008), 136-162. Pdf, arXiv, MathSciNet.

·       Le groupe des traces de Poisson de la variété quotient h+h^*/W en rang 2, en collaboration avec Jacques Alev. Comm. Algebra 37 (2009), no. 1, 368-388. Pdf, arXiv, MathSciNet.

·       L'algèbre des invariants d'un groupe de Coxeter agissant sur un multiple de sa représentation standard. Pdf, arXiv

·       Étude de l'algèbre de Lie double des arbres enracinés décorés. Adv.Math. 208 (2007), no.2, 877-904. Pdf, MathSciNet.

·       Bidendriform bialgebras, trees, and free quasi-symmetric functions. J.Pure Appl. Algebra 209 (2007), no. 2, 439-459. Pdf, arXiv, MathSciNet.

·       Quantization of the Hopf algebras of planar decorated rooted trees. Pdf.

·       Quantifications des algèbres de Hopf d'arbres plans décorés et lien avec les groupes quantiques. Bull. Sci. Math. 127 (2003), no. 6, 505-548. Pdf, MathSciNet.

·       Finite-dimensional comodules over the Hopf algebra of rooted trees. J. Algebra 255 (2002), no. 1, 89-120. Pdf, arXiv, MathSciNet.

·       Les algèbres de Hopf des arbres enracinés décorés. II. Bull. Sci. Math. 126 (2002), no. 4, 249-288. Pdf, arXiv, MathSciNet.

·       Les algèbres de Hopf des arbres enracinés décorés. I. Bull. Sci. Math. 126 (2002), no. 3, 193-239. Pdf, arXiv, MathSciNet.