GD
Gérard Duchamp
math.COcs.SCmath.MPmath-phquant-phcs.DMhep-thcs.MAmath.CAmath.NT
On Valency
published · living versionsW_svex6pj3·v1 · currentpublished
Three variations on the linear independence of grouplikes in a coalgebra
with Darij Grinberg, Vincel Minh
1 version
Preprints & journals
84 papers in the corpus · 2001–2024Elementary methods for splitting representations of Rook monoids: a gentle introduction to groupoids2410.23731v1 · G'erard Henry Edmond Duchamp (LIPN), Joseph Ben Geloun (LIPN), Christophe Tollu (LIPN)2024 · 0 citationsarXiv
About enveloping algebras of direct sums2405.01092v2 · G'erard Henry Edmond Duchamp (LIPN), Christophe Tollu (LIPN), Jean-Gabriel Luque (GR2IF) et al.2024 · 0 citationsarXiv
Elementary remarks about Pisano periods2206.07095v2 · G'erard Henry Edmond Duchamp (LIPN), Pierre Simonnet (UDC)2022 · 0 citationsarXiv
Towards a Theory of Domains for Harmonic Functions and its Symbolic Counterpart2110.13743v1 · van Chien Bui, G'erard Duchamp (LIPN), Quoc Hoan Ngo et al.2021 · 0 citationsarXiv
Three variations on the linear independence of grouplikes in a coalgebra2009.10970v5 · G'erard Duchamp (LIPN), Darij Grinberg, Vincel Minh2020 · 0 citationsarXivon Valency
A local Theory of Domains and its (Noncommutative) Symbolic Counterpart2009.05125v2 · V.C. Bui, G.H.E. Duchamp, V. Hoang Ngoc Minh et al.2020 · 1 citationarXiv
Towards a noncommutative Picard-Vessiot theory2008.10872v5 · G. Duchamp (LIPN), Viincel Hoang Ngoc Minh, Vu Nguyen Dinh et al.2020 · 2 citationsarXiv
A localized version of the basic triangle theorem1908.03327v3 · G'erard Duchamp (LIPN), Nihar Gargava, Hoang Ngoc Minh (LIPN) et al.2019 · 0 citationsarXiv
Kleene stars of the plane, polylogarithms and symmetries1811.09091v2 · G'erard Henry Edmond Duchamp (LIPN), Vincel Hoang Ngoc Minh, Ngo Quoc Hoan2018 · 1 citationTheoretical Computer Science, Elsevier, 2019, 800, pp.52-72
Operational Methods in the Study of Sobolev-Jacobi Polynomials1810.09793v2 · Nicolas Behr, Giuseppe Dattoli, G'erard H. E. Duchamp et al.2018 · 10 citationsMathematics, vol. 7, no. 2, p. 124, Jan. 2019
Explicit formulae for all higher order exponential lacunary generating functions of Hermite polynomials1806.08417v1 · Nicolas Behr, G'erard H. E. Duchamp, Karol A. Penson2018 · 4 citationsarXiv
Combinatorics of chemical reaction systems1712.06575v2 · Nicolas Behr, G'erard H. E. Duchamp, Karol A. Penson2017 · 6 citationsarXiv
On Drinfel'd associators1705.01882v1 · G'erard Duchamp (LIPN), Ngoc Minh (LIPN), K Penson (LPTMC)2017 · 0 citationsarXiv
Mathematical renormalization in quantum electrodynamics via noncommutative generating series1702.08550v1 · G'erard Henry Edmond Duchamp (LIPN), Vincel Hoang Ngoc Minh (LIPN), Quoc Hoan Ngo (LIPN) et al.2017 · 7 citationsarXiv
Structure of Polyzetas and Explicit Representation on Transcendence Bases of Shuffle and Stuffle Algebras1612.06011v1 · Van Chien Bui, Gerard H. E. Duchamp, Vincel Hoang Ngoc Minh2016 · 8 citationsarXiv
Harmonic sums and polylogarithms at non-positive multi-indices1611.09683v1 · G'erard Duchamp (LIPN), Hoang Ngoc (LIPN), Ngo Quoc (LIPN)2016 · 14 citationsarXiv
The stretched exponential behavior and its underlying dynamics. The phenomenological approach1603.06066v5 · K. G'orska, A. Horzela, K. A. Penson et al.2016 · 10 citationsFractional Calculus and Applied Analysis vol. 20(1), 260 (2017)
The algebra of Kleene stars of the plane and polylogarithms1602.02801v2 · Ngoc Hoang (LIPN), G'erard Duchamp (LIPN), Hoang Ngoc Minh (LIPN)2016 · 0 citationsarXiv
The mechanics of shuffle products and their siblings1512.01637v1 · Jean-Yves Enjalbert (LIPN), Vincel Hoang (LIPN), G'erard H. E. Duchamp (LIPN) et al.2015 · 0 citationsarXiv
(Pure) transcendence bases in -deformed shuffle bialgebras1507.01089v2 · Van Chien Bui (LIPN), G'erard H.E. Duchamp (LIPN), Quoc Hoan Ngo (LIPN) et al.2015 · 4 citationsSeminaire Lotharingien de Combinatoire, Universit{\'e} Louis Pasteur, 2015, 74, pp.1-31
Combinatorial interpretation and proof of Glaisher-Crofton identity1407.4960v1 · Pawel Blasiak, Gerard H. E. Duchamp, Andrzej Horzela et al.2014 · 2 citationsAdv. Math. Phys. 2018, Article ID 9575626 (2018)
Renormalization group-like proof of the universality of the Tutte polynomial for matroids1310.5516v1 · G. H. E.Duchamp, N. Hoang-Nghia, T. Krajewski et al.2013 · 2 citationsDiscrete Mathematics & Theoretical Computer Science Proceedings FPSAC 2013, pag. 397-408 (2013)
A selection-quotient process for packed word Hopf algebra1310.4418v1 · G. H.E. Duchamp, N. Hoang-Nghia, A. Tanasa2013 · 1 citationLecture Notes in Computer Science, volume 8080, Pages 223-234, 2013
A combinatorial non-commutative Hopf algebra of graphs1307.3928v3 · G. H. E. Duchamp, L. Foissy, N. Hoang-Nghia et al.2013 · 5 citationsDiscrete Mathematics & Theoretical Computer Science, Vol 16, No 1 (2014) 356-370
Dual bases for non commutative symmetric and quasi-symmetric functions via monoidal factorization1305.4447v1 · G'erard Henry Edmond Duchamp (LIPN), Ladji Kane (LIPN), Vincel Hoang Ngoc Minh (LIPN) et al.2013 · 0 citationsarXiv
Schützenberger's factorization on the (completed) Hopf algebra of stuffle product1305.4450v1 · Chen Bui, G'erard Henry Edmond Duchamp (LIPN), Vincel Hoang Ngoc Minh (LIPN)2013 · 6 citationsarXiv
Finite Decomposition Semigroups1303.3913v1 · Matthieu Deneufchatel, G'erard H. E. Duchamp2013 · 0 citationsarXiv
Combinatorics of -deformed stuffle Hopf algebras1302.5391v7 · G'erard Henry Edmond Duchamp (LIPN), Vincel Hoang Ngoc Minh (LIPN), Christophe Tollu (LIPN) et al.2013 · 0 citationsarXiv
Recipe theorem for the Tutte polynomial for matroids, renormalization group-like approach1301.0782v1 · G'erard H. E. Duchamp, Nguyen Hoang-Nghia, Thomas Krajewski et al.2013 · 16 citationsAdvances in Applied Mathematics 51 (2013), 345-358
A word Hopf algebra based on the selection/quotient principle1207.6522v2 · G. H. E. Duchamp, N. Hoang-Nghia, A. Tanasa2012 · 2 citationsSeminaire Lotharingien de Combinatoire, B68c (2013)
Degrees of entanglement for multipartite systems1205.4958v2 · A. I. Solomon, C.-L. Ho, G. H. E. Duchamp2012 · 0 citationsJ. Phys. A: Math. Theor. 46 (2013) 075302
A generic Hopf algebra for quantum statistical mechanics1203.1446v1 · Allan I. Solomon, Gerard E. H. Duchamp, Pawel Blasiak et al.2012 · 1 citationPhysica Scripta 82 038115 (2010)
Operator solutions for fractional Fokker-Planck equations.22587069 · Górska, K, Penson, K A, Babusci, D et al.2012 · 28 citationsPhysical review. E, Statistical, nonlinear, and soft matter physics. 2012;85(3 Pt 1):031138
Radford bases and Schützenberger's Factorizations1111.6759v2 · Matthieu Deneufchatel, G'erard H. E. Duchamp, Vincel Hoang Ngoc Minh2011 · 1 citationarXiv
Generalized Bargmann functions, their growth and von Neumann lattices1111.0889v2 · A. Vourdas, K. A. Penson, G. H. E. Duchamp et al.2011 · 4 citationsJ. Phys. A: Math. Theor. vol. 45, 244031 (2012)
Definite integrals and operational methods1105.5967v3 · D. Babusci, G. Dattoli, G. H. E. Duchamp et al.2011 · 7 citationsApplied Mathematics and Computation 219 (2012) 3017-3021
The Ramanujan master theorem and its implications for special functions1104.3406v1 · K. Gorska, D. Babusci, G. Dattoli et al.2011 · 22 citationsApplied Mathematics and Computation 218 (2012) 11466-11471
Independence of hyperlogarithms over function fields via algebraic combinatorics1101.4497v3 · Matthieu Deneufchatel (LIPN), G'erard Henry Edmond Duchamp (LIPN), Vincel Hoang Ngoc Minh (LIPN) et al.2011 · 32 citationsarXiv
The Rayleigh-Schrödinger perturbation series of quasi-degenerate systems1011.1751v1 · Christian Brouder (IMPMC), G'erard H. E. Duchamp (LIPN), Fr'ed'eric Patras (JAD) et al.2010 · 10 citationsInternational Journal of Quantum Chemistry 112, 10 (2012) 2256-2266
An interface between physics and number theory1011.0523v2 · G'erard Henry Edmond Duchamp (LIPN), Vincel Hoang Ngoc Minh (LIPN), Allan I. Solomon (LPTMC) et al.2010 · 4 citationsarXiv
From Quantum Mechanics to Quantum Field Theory: The Hopf route1011.0524v1 · Allan I. Solomon (LPTMC), G'erard Henry Edmond Duchamp (LIPN), Pawel Blasiak et al.2010 · 3 citationsJ.Phys.Conf.Ser.284:012055,2011
Quasiclassical Asymptotics and Coherent States for Bounded Discrete Spectra1007.2617v2 · K. Gorska, K. A. Penson, A. Horzela et al.2010 · 7 citationsJ.Math. Phys. 51, 122102 (2010)
Generation of coherent states of photon-added type via pathway of eigenfunctions1007.2418v1 · K. Gorska, K. A. Penson, G. H. E. Duchamp2010 · 3 citationsJ. Phys. A: Math. Theor. 43, 375303 (2010)
Partial monoids: associativity and confluence1002.2166v1 · Laurent Poinsot (LIPN), G'erard Duchamp (LIPN), Christophe Tollu (LIPN)2010 · 5 citationsJournal of Pure and Applied Mathematics 3, 2 (2010) 265-285
Combinatorial Algebra for second-quantized Quantum Theory1001.4964v1 · P. Blasiak, G. H. E. Duchamp, A. I. Solomon et al.2010 · 20 citationsarXiv
Hopf algebras: motivations and examples0912.3866v1 · G. H. E. Duchamp (LIPN), P. Blasiak, A. Horzela et al.2009 · 0 citationsarXiv
Möbius inversion formula for monoids with zero0911.4821v2 · Laurent Poinsot (LIPN), G'erard Duchamp (LIPN), Christophe Tollu (LIPN)2009 · 4 citationsSemigroup Forum (2010) 1-15
Statistics on Graphs, Exponential Formula and Combinatorial Physics0910.0695v2 · L. Poinsot (LIPN), G. H. E. Duchamp (LIPN), S. Goodenough (LIPN) et al.2009 · 2 citationsJournal of Nonlinear Systems and Applications 1, 1 (2010) 58-62
On certain non-unique solutions of the Stieltjes moment problem0909.4846v1 · K. A. Penson (LPTMC), P. Blasiak, G. H. E. Duchamp (LIPN) et al.2009 · 15 citationsDiscrete Mathematics and Theoretical Computer Science 12, 2 (2010) 295-306
Ladder Operators and Endomorphisms in Combinatorial Physics0908.2332v2 · G'erard Henry Edmond Duchamp (LIPN), Laurent Poinsot (LIPN), Allan I. Solomon (LPTMC) et al.2009 · 6 citationsDMTCS 12, 2 (2010) 1
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