On the number of words with restrictions on the number of symbols

Autor: Verónica Becher, Eda Cesaratto

We show that, in an alphabet of $n$ symbols, the number of words of length $n$ whose number of different symbols is away from $(1-1/e)n$, which is the value expected by the Poisson distribution, has exponential decay in $n$. We use Laplace's method f

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5a43422d6565acc6e1642e186e431516
http://arxiv.org/abs/2105.12813

The distribution of factorization patterns on linear families of polynomials over a finite field

Autor: Guillermo Matera, Eda Cesaratto, Mariana Pérez

Publikováno v: CONICET Digital (CONICET)
Consejo Nacional de Investigaciones Científicas y Técnicas
instacron:CONICET

We obtain estimates on the number $|\mathcal{A}_{\boldsymbol{\lambda}}|$ of elements on a linear family $\mathcal{A}$ of monic polynomials of $\mathbb{F}_q[T]$ of degree $n$ having factorization pattern $\boldsymbol{\lambda}:=1^{\lambda_1}2^{\lambda_

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::59f80f4cd9e5b409e679c6a54f9ac743
https://link.springer.com/article/10.1007/s00493-015-3330-5

Irreducibility criteria for reciprocal polynomials and applications

Autor: Antonio Cafure, Eda Cesaratto

We present criteria for determining irreducibility of reciprocal polynomials over the field of rational numbers. We also obtain some combinatorial results concerning the irreducibility of reciprocal polynomials. As a consequence of our approach, we a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cb1560ad7f42ab9a25bb3c27447e0c6f
https://www.tandfonline.com/doi/abs/10.4169/amer.math.monthly.124.1.37

Pseudo-randomness of a random Kronecker sequence. An instance of dynamical analysis

Autor: Eda Cesaratto, Brigitte Vallée

Publikováno v: Combinatorics, Words and Symbolic Dynamics
Edited by V. Berthé and M. Rigo. Combinatorics, Words and Symbolic Dynamics, Cambridge University Press, pp.401-442, 2016, 9781139924733. ⟨10.1017/CBO9781139924733.012⟩

Introduction A measure of randomness on the unit interval ℐ := [0,1] tests how a sequence X ⊂ ℐ differs from a ‘truly random’ sequence. See books (Drmota and Tichy, 1997; Kuipers and Niederreiter, 1974) for a general discussion on the subje

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3c176884b4a069e7638d2cb7c6eb9e99
https://hal.archives-ouvertes.fr/hal-01578308

Gaussian distribution of trie depth for strongly tame sources

Autor: Eda Cesaratto, Brigitte Vallée

Publikováno v: Combinatorics, Probability and Computing
Combinatorics, Probability and Computing, Cambridge University Press (CUP), 2015, 24 (01), pp.54-103. ⟨10.1017/S0963548314000741⟩

The depth of a trie has been deeply studied when the source which produces the words is a simple source (a memoryless source or a Markov chain). When a source is simple but not an unbiased memoryless source, the expectation and the variance are both

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a6203e64c32eda14749fa350d30b620b
https://www.cambridge.org/core/journals/combinatorics-probability-and-computing/article/div-classtitlegaussian-distribution-of-trie-depth-for-strongly-tame-sourcesdiv/83E2FECEDBCF32D707D0EFCE926D20B6