Zobrazeno 1 - 10
of 249
pro vyhledávání: '"Singer, Michael F."'
For given multivariate functions specified by algebraic, differential or difference equations, the separability problem is to decide whether they satisfy linear differential or difference equations in one variable. In this paper, we will explain how
Externí odkaz:
http://arxiv.org/abs/2102.03693
Telescopers for a function are linear differential (resp. difference) operators annihilated by the definite integral (resp. definite sum) of this function. They play a key role in Wilf-Zeilberger theory and algorithms for computing them have been ext
Externí odkaz:
http://arxiv.org/abs/2101.06576
Autor:
Roques, Julien, Singer, Michael F.
We study the form of possible algebraic relations between functions satisfying linear differential equations. In particular , if f and g satisfy linear differential equations and are algebraically dependent, we give conditions on the differential Gal
Externí odkaz:
http://arxiv.org/abs/2011.01717
Autor:
Hardouin, Charlotte, Singer, Michael F
We refine necessary and sufficient conditions for the generating series of a weighted model of a quarter plane walk to be differentially algebraic. In addition, we give algorithms based on the theory of Mordell-Weil lattices, that, for each weighted
Externí odkaz:
http://arxiv.org/abs/2010.00963
Publikováno v:
Springer Proceedings in Mathematics and Statistics. Vol. 373, (2021), p.61-89
The kernel method is an essential tool for the study of generating series of walks in the quarter plane. This method involves equating to zero a certain polynomial, the kernel polynomial, and using properties of the curve, the kernel curve, this defi
Externí odkaz:
http://arxiv.org/abs/2004.01035
Autor:
Hubert, Evelyne, Singer, Michael F.
Sparse interpolation} refers to the exact recovery of a function as a short linear combination of basis functions from a limited number of evaluations. For multivariate functions, the case of the monomial basis is well studied, as is now the basis of
Externí odkaz:
http://arxiv.org/abs/2001.09144
Akademický článek
Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
K zobrazení výsledku je třeba se přihlásit.
K zobrazení výsledku je třeba se přihlásit.
Publikováno v:
Journal of Combinatorial Theory, Series A, (2020), vol. 174, p. 105251
We use Galois theory of difference equations to study the nature of the generating series of (weighted) walks in the quarter plane with genus zero kernel curve. Using this approach, we prove that the generating series do not satisfy any nontrivial (p
Externí odkaz:
http://arxiv.org/abs/1710.02848
Publikováno v:
Inventiones Mathematicae, 213 (2018), no.1, 139-203
In the present paper, we introduce a new approach, relying on the Galois theory of difference equations, to study the nature of the generating series of walks in the quarter plane. Using this approach, we are not only able to recover many of the rece
Externí odkaz:
http://arxiv.org/abs/1702.04696
Autor:
Arreche, Carlos E., Singer, Michael F.
Publikováno v:
Journal of Algebra, 480:423-449, (2017)
We consider first-order linear difference systems over $\mathbb{C}(x)$, with respect to a difference operator $\sigma$ that is either a shift $\sigma:x\mapsto x+1$, $q$-dilation $\sigma:x\mapsto qx$ with $q\in{\mathbb{C}^\times}$ not a root of unity,
Externí odkaz:
http://arxiv.org/abs/1608.00015