scholarly journals Revisiting regular sequences in light of rational base numeration systems

2022 ◽  
Vol 345 (3) ◽  
pp. 112735
Author(s):  
Michel Rigo ◽  
Manon Stipulanti
Keyword(s):  
Regular Sequences ◽  
Numeration Systems

scholarly journals Regular sequences and synchronized sequences in abstract numeration systems

2022 ◽  
Vol 101 ◽  
pp. 103475
Author(s):  
Émilie Charlier ◽  
Célia Cisternino ◽  
Manon Stipulanti
Keyword(s):  
Regular Sequences ◽  
Numeration Systems

scholarly journals ENUMERATION AND DECIDABLE PROPERTIES OF AUTOMATIC SEQUENCES

2012 ◽  
Vol 23 (05) ◽  
pp. 1035-1066 ◽  
Author(s):  
ÉMILIE CHARLIER ◽  
NARAD RAMPERSAD ◽  
JEFFREY SHALLIT
Keyword(s):  
Automatic Sequences ◽  
Regular Sequences ◽  
Numeration Systems

We show that various aspects of k-automatic sequences — such as having an unbordered factor of length n — are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give some new characterizations of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems.

Ubiquity of relative regular sequences and proper sequences

K-Theory ◽  
1994 ◽  
Vol 8 (1) ◽  
pp. 81-106 ◽  
Author(s):  
Mihai Cipu ◽  
Mario Fiorentini
Keyword(s):  
Regular Sequences

An extension of the Cobham-Semënov Theorem

2000 ◽  
Vol 65 (1) ◽  
pp. 201-211 ◽  
Author(s):  
Alexis Bès
Keyword(s):  
Characteristic Polynomial ◽  
Minimal Polynomial ◽  
Pisot Numbers ◽  
Numeration Systems

AbstractLet θ, θ′ be two multiplicatively independent Pisot numbers, and letU,U′ be two linear numeration systems whose characteristic polynomial is the minimal polynomial of θ and θ′, respectively. For everyn≥ 1, ifA⊆ ℕnisU-andU′ -recognizable thenAis definable in 〈ℕ: + 〉.

scholarly journals Linear numeration systems of order two

1988 ◽  
Vol 77 (3) ◽  
pp. 233-259 ◽  
Author(s):  
Christiane Frougny
Keyword(s):  
Numeration Systems

The Main Case for Regular Sequences

2001 ◽  
pp. 96-104
Author(s):  
Günter Scheja ◽  
Uwe Storch
Keyword(s):  
Regular Sequences

The Main Case for Generic Regular Sequences

2001 ◽  
pp. 85-95
Author(s):  
Günter Scheja ◽  
Uwe Storch
Keyword(s):  
Regular Sequences

scholarly journals Some New Methods in the Theory of $m$-Quasi-Invariants

10.37236/1877 ◽  
2005 ◽  
Vol 11 (2) ◽  
Author(s):  
J. Bell ◽  
A. M. Garsia ◽  
N. Wallach
Keyword(s):  
Symmetric Functions ◽  
Free Module ◽  
Finitely Generated ◽  
Graded Algebras ◽  
New Approach ◽  
Elementary Symmetric Functions ◽  
New Methods ◽  
Regular Sequences

We introduce here a new approach to the study of $m$-quasi-invariants. This approach consists in representing $m$-quasi-invariants as $N^{tuples}$ of invariants. Then conditions are sought which characterize such $N^{tuples}$. We study here the case of $S_3$ $m$-quasi-invariants. This leads to an interesting free module of triplets of polynomials in the elementary symmetric functions $e_1,e_2,e_3$ which explains certain observed properties of $S_3$ $m$-quasi-invariants. We also use basic results on finitely generated graded algebras to derive some general facts about regular sequences of $S_n$ $m$-quasi-invariants

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