Geodesic
On a matrix representation for polynomially recursive sequences
Christophe Reutenauer1
1Université du Québec à Montréal
The electronic journal of combinatorics, Tome 19 (2012) no. 3
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In this article we derive several consequences of a matricial characterization of P-recursive sequences. This characterization leads to canonical representations of these sequences. We show their uniqueness for a given sequence, up to similarity. We study their properties: operations, closed forms, d'Alembertian sequences, field extensions, positivity, extension of the sequence to $\mathbb Z$, difference Galois group.
DOI : 10.37236/2721
Classification : 05A19, 05A15, 12H10, 33D15, 39A70
Mots-clés : P-recursive, matrix representation, Galois theory

Christophe Reutenauer  1

1 Université du Québec à Montréal 
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     title = {On a matrix representation for polynomially recursive sequences},
     journal = {The electronic journal of combinatorics},
     year = {2012},
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     number = {3},
     doi = {10.37236/2721},
     zbl = {1298.05039},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2721/}
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Christophe Reutenauer. On a matrix representation for polynomially recursive sequences. The electronic journal of combinatorics, Tome 19 (2012) no. 3. doi: 10.37236/2721

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