Zobrazeno 1 - 10
of 30
pro vyhledávání: '"Minh, Vincel"'
In this paper, we begin by reviewing the calculus induced by the framework of [10]. In there, we extended Polylogarithm functions over a subalgebra of noncommutative rational power series, recognizable by finite state (multiplicity) automata over the
Externí odkaz:
http://arxiv.org/abs/2110.13743
The grouplike elements of a coalgebra over a field are known to be linearly independent over said field. Here we prove three variants of this result. One is a generalization to coalgebras over a commutative ring (in which case the linear independence
Externí odkaz:
http://arxiv.org/abs/2009.10970
Publikováno v:
Theoretical Computer Science, Elsevier, 2019, 800, pp.52-72
We extend the definition and construct several bases for polylogarithms Li T , where T are some series, recognizable by a finite state (multiplicity) automaton of alphabet 4 X = {x 0 , x 1 }. The kernel of this new "polylogarithmic map" Li $\bullet$
Externí odkaz:
http://arxiv.org/abs/1811.09091
Autor:
Duchamp, Gérard Henry Edmond, Minh, Vincel Hoang Ngoc, Ngo, Quoc Hoan, Penson, Karol A., Simonnet, Pierre
In this work, we focus on on the approach by noncommutative formal power series to study the combinatorial aspects of the renormalization at the singularities in $\{0,1,+\infty\}$ of the solutions of nonlinear differential equations involved in quant
Externí odkaz:
http://arxiv.org/abs/1702.08550
Polyzetas, indexed by words, satisfy shuffle and quasi-shuffle identities. In this respect, one can explore the multiplicative and algorithmic (locally finite) properties of their generating series. In this paper, we construct pairs of bases in duali
Externí odkaz:
http://arxiv.org/abs/1612.06011
Autor:
Bui, Van Chiên, Duchamp, Gérard H. E., Ngô, Quoc Hoan, Minh, Vincel Hoang Ngoc, Tollu, Christophe
Publikováno v:
Seminaire Lotharingien de Combinatoire, Universit{\'e} Louis Pasteur, 2015, 74, pp.1-31
Computations with integro-differential operators are often carried out in an associative algebra with unit, and they are essentially non-commutative computations. By adjoining a cocommutative co-product, one can have those operators perform act on a
Externí odkaz:
http://arxiv.org/abs/1507.01089
In order to extend the Sch\"utzenberger's factorization, the combinatorial Hopf algebra of the $q$-stuffles product is developed systematically in a parallel way with that of the shuffle product and and in emphasizing the Lie elements as studied by R
Externí odkaz:
http://arxiv.org/abs/1305.4450
In this work, an effective construction, via Sch\"utzenberger's monoidal factorization, of dual bases for the non commutative symmetric and quasi-symmetric functions is proposed.
Externí odkaz:
http://arxiv.org/abs/1305.4447
Autor:
Duchamp, Gérard Henry Edmond, Minh, Vincel Hoang Ngoc, Tollu, Christophe, Chiên, Bùi, Nghia, Nguyen Hoang
In order to extend the Sch\"utzenberger's factorization to general perturbations, the combinatorial aspects of the Hopf algebra of the $\phi$-deformed stuffle product is developed systematically in a parallel way with those of the shuffle product.
Externí odkaz:
http://arxiv.org/abs/1302.5391
In this paper, we present Sch\"utzenberger's factorization in different combinatorial contexts and show that its validity is not restricted to these cases but can be extended to every Lie algebra endowed with an ordered basis. We also expose some ele
Externí odkaz:
http://arxiv.org/abs/1111.6759