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pro vyhledávání: '"Arreche, Carlos E."'
Complex reflection groups comprise a generalization of Weyl groups of semisimple Lie algebras, and even more generally of finite Coxeter groups. They have been heavily studied since their introduction and complete classification in the 1950s by Sheph
Externí odkaz:
http://arxiv.org/abs/2407.08419
Autor:
Arreche, Carlos E., Sitaula, Hari P.
In 2012 Chen and Singer introduced the notion of discrete residues for rational functions as a complete obstruction to rational summability. More explicitly, for a given rational function f(x), there exists a rational function g(x) such that f(x) = g
Externí odkaz:
http://arxiv.org/abs/2402.07328
Autor:
Arnold, Maxim, Arreche, Carlos E.
The symmedian point of a triangle enjoys several geometric and optimality properties, which also serve to define it. We develop a new dynamical coordinatization of the symmedian, which naturally generalizes to other ideal hyperbolic polygons beyond t
Externí odkaz:
http://arxiv.org/abs/2311.14194
Autor:
Arreche, Carlos E., Zhang, Yi
Recently we constructed Mahler discrete residues for rational functions and showed they comprise a complete obstruction to the Mahler summability problem of deciding whether a given rational function $f(x)$ is of the form $g(x^p)-g(x)$ for some ratio
Externí odkaz:
http://arxiv.org/abs/2308.16765
Autor:
Arreche, Carlos E., Zhang, Yi
Publikováno v:
Proceedings of ISSAC 2022 (2022), pp. 525-533
We construct Mahler discrete residues for rational functions and show that they comprise a complete obstruction to the Mahler summability problem of deciding whether a given rational function $f(x)$ is of the form $g(x^p)-g(x)$ for some rational func
Externí odkaz:
http://arxiv.org/abs/2202.09805
Autor:
Arreche, Carlos E., Zhang, Yi
We apply the differential Galois theory for difference equations developed by Hardouin and Singer to compute the differential Galois group for a second-order linear $q$-difference equation with rational function coefficients. This Galois group encode
Externí odkaz:
http://arxiv.org/abs/2009.14026
We study normal reflection subgroups of complex reflection groups. Our approach leads to a refinement of a theorem of Orlik and Solomon to the effect that the generating function for fixed-space dimension over a reflection group is a product of linea
Externí odkaz:
http://arxiv.org/abs/2007.09778
Autor:
Arreche, Carlos E., Williams, Nathan
We study normal reflection subgroups of complex reflection groups. Our point of view leads to a refinement of a theorem of Orlik and Solomon to the effect that the generating function for fixed-space dimension over a reflection group is a product of
Externí odkaz:
http://arxiv.org/abs/2006.06575
Akademický článek
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Publikováno v:
Journal de l'\'Ecole polytechnique - Math\'ematiques. (2021), vol. 8, p. 147-168
We develop general criteria that ensure that any non-zero solution of a given second-order difference equation is differentially transcendental, which apply uniformly in particular cases of interest, such as shift difference equations, q-dilation dif
Externí odkaz:
http://arxiv.org/abs/1809.05416