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It was recently conjectured that every component of a discrete-time rational dynamical system is a solution to an algebraic difference equation that is linear in its highest-shift term (a quasi-linear equation). We prove that the conjecture holds in
Externí odkaz:
http://arxiv.org/abs/2404.19136
Autor:
Tabuguia, Bertrand Teguia
Take a multiplicative monoid of sequences in which the multiplication is given by Hadamard product. The set of linear combinations of interleaving monoid elements then yields a ring. For hypergeometric sequences, the resulting ring is a subring of th
Externí odkaz:
http://arxiv.org/abs/2404.10143
Autor:
Tabuguia, Bertrand Teguia
We introduce hypergeometric-type sequences. They are linear combinations of interlaced hypergeometric sequences (of arbitrary interlacements). We prove that they form a subring of the ring of holonomic sequences. An interesting family of sequences in
Externí odkaz:
http://arxiv.org/abs/2401.00256
Autor:
Tabuguia, Bertrand Teguia
We are concerned with the arithmetic of solutions to ordinary or partial nonlinear differential equations which are algebraic in the indeterminates and their derivatives. We call these solutions D-algebraic functions, and their equations are algebrai
Externí odkaz:
http://arxiv.org/abs/2305.00702
Autor:
Tabuguia, Bertrand Teguia
A function is differentially algebraic (or simply D-algebraic) if there is a polynomial relationship between some of its derivatives and the indeterminate variable. Many functions in the sciences, such as Mathieu functions, the Weierstrass elliptic f
Externí odkaz:
http://arxiv.org/abs/2304.09675
Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We present algo
Externí odkaz:
http://arxiv.org/abs/2301.02512
Autor:
Tabuguia, Bertrand Teguia
By holonomic guessing, we denote the process of finding a linear differential equation with polynomial coefficients satisfied by the generating function of a sequence, for which only a few first terms are known. Holonomic guessing has been used in co
Externí odkaz:
http://arxiv.org/abs/2207.01037
Linear recurrence equations with constant coefficients define the power series coefficients of rational functions. However, one usually prefers to have an explicit formula for the sequence of coefficients, provided that such a formula is "simple" eno
Externí odkaz:
http://arxiv.org/abs/2207.01031
Let $\left(u(n)\right)_{n\in\mathbb{N}}$ be an arithmetic progression of natural integers in base $b\in\mathbb{N}\setminus \{0,1\}$. We consider the following sequences: $s(n)=\overline{u(0)u(1)\cdots u(n) }^b$ formed by concatenating the first $n+1$
Externí odkaz:
http://arxiv.org/abs/2201.07127