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Erschienen in:
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2016 | OriginalPaper | Buchkapitel

2. Generic Linear Recurrence Sequences

verfasst von : Letterio Gatto, Parham Salehyan

Erschienen in: Hasse-Schmidt Derivations on Grassmann Algebras

Verlag: Springer International Publishing

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Abstract

Let A be a commutative ring with unit and M any A-module. An M-valued linear recurrence sequence (LRS) generalizes the sequence of powers of the roots of a given monic polynomial with A-coefficients. A generic LRS is a linear recurrence sequence with indeterminate coefficients. A main character of this chapter, as of the entire book, is the ring \(B_{r}:= \mathbb{Z}[e_{1},\ldots,e_{r}]\), thought of as a free polynomial algebra generated by the coefficients of a generic LRS of order r ≥ 1. The name of the indeterminates, (e 1, …, e r ), is reminiscent of the elementary symmetric polynomials in r variables. The ring B r will later be bestowed the more ambitious task of approximating the bosonic Fock representation of the oscillator Heisenberg algebra.

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Vorheriges Kapitel Prologue
Nächstes Kapitel Algebras and Derivations
Fußnoten
1
Pierre-Simon, marquis de Laplace, Beaumont-en-Auge, Normandy, 1749–Paris, 1897. Mathematician and astronomer, he wrote the celebrated celestial mechanics . Asked by Napoleon why there was no mention to God in his treatise, as was customary at the time, he answered: je n’avais pas besoin de cette hypothèse-là: I didn’t need that hypothesis.
 
2
Leonardo Pisano, known as Fibonacci (Pisa, 1170–1240), wrote the famous Liber Abaci in 1202 where the name ‘zero’ comes from ‘Zephyrus’, a wind blowing from the West.
 
3
Mario Merz (Milano, 1925–2003) was a painter and sculptor who used poor materials for his creations (http://​fondazionemerz.​org/​en/​mario-merz/​).
 
4
The flight of numbers
 
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Metadaten
Titel
Generic Linear Recurrence Sequences
verfasst von
Letterio Gatto
Parham Salehyan
Copyright-Jahr
2016
Buch
Hasse-Schmidt Derivations on Grassmann Algebras

Print ISBN: 978-3-319-31841-7

Electronic ISBN: 978-3-319-31842-4

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-319-31842-4_2