Zobrazeno 1 - 10
of 205
pro vyhledávání: '"Allouche, Jean-Paul"'
In combinatorics on words, the well-studied factor complexity function $\rho_{\bf x}$ of a sequence ${\bf x}$ over a finite alphabet counts, for any nonnegative integer $n$, the number of distinct length-$n$ factors of $\mathbf{x}$. In this paper, we
Externí odkaz:
http://arxiv.org/abs/2406.09302
Ellipsephic or Kempner-like harmonic series are series of inverses of integers whose expansion in base $B$, for some $B \geq 2$, contains no occurrence of some fixed digit or some fixed block of digits. A prototypical example was proposed by Kempner
Externí odkaz:
http://arxiv.org/abs/2403.05678
Generating series are crucial in enumerative combinatorics, analytic combinatorics, and combinatorics on words. Though it might seem at first view that generating Dirichlet series are less used in these fields than ordinary and exponential generating
Externí odkaz:
http://arxiv.org/abs/2401.13524
Autor:
Allouche, Jean-Paul, Stipulanti, Manon
Publikováno v:
Communications in Mathematics, Volume 33 (2025), Issue 2 (Special issue: Numeration, Liège 2023, dedicated to the 75th birthday of professor Christiane Frougny) (May 9, 2024) cm:12610
We revisit and generalize inequalities for the summatory function of the sum of digits in a given integer base. We prove that several known results can be deduced from a theorem in a 2023 paper by Mohanty, Greenbury, Sarkany, Narayanan, Dingle, Ahner
Externí odkaz:
http://arxiv.org/abs/2311.16806
Autor:
Allouche, Jean-Paul, Morin, Claude
Inspired by a question asked on the list {\tt mathfun}, we revisit {\em Kempner-like series}, i.e., harmonic sums $\sum' 1/n$ where the integers $n$ in the summation have ``restricted'' digits. First we give a short proof that $\lim_{k \to \infty}(\s
Externí odkaz:
http://arxiv.org/abs/2305.18180
Publikováno v:
Beyond quasicrystals (Les Houches, 1994), 293--367, Springer, Berlin, 1995
In the following pages we discuss infinite sequences defined on a finite alphabet, and more specially those which are generated by finite automata. We have divided our paper into seven parts which are more or less self-contained. Needless to say, we
Externí odkaz:
http://arxiv.org/abs/2212.08857
Autor:
Allouche, Jean-Paul, Zeilberger, Doron
We show that identities involving trigonometric sums recently proved by Harshitha, Vasuki and Yathirajsharma, using Ramanujan's theory of theta functions, were either already in the literature or can be proved easily by adapting results that can be f
Externí odkaz:
http://arxiv.org/abs/2204.08228
Autor:
Allouche, Jean-Paul, Shallit, Jeffrey
First we reprove two results in additive number theory due to Dombi and Chen & Wang, respectively, on the number of representations of n as the sum of two odious or evil numbers, using techniques from automata theory and logic. We also use this techn
Externí odkaz:
http://arxiv.org/abs/2112.13627
Publikováno v:
In Journal of Algebra 1 February 2024 639:708-719