Name
Abstract | ||
|---|---|---|
A D0L-system is a triple (A,�,w) where A is a finite alphabet, � is an endo- morphism of the free monoid over A, and w is a word over A. The D0L-sequence generated by (A,�,w) is the sequence of words (w,�(w),�(�(w)),�(�(�(w))),... ). The corresponding sequence of lengths, that is the function mapping each integer n ≥ 0 to |�n(w)|, is called the growth function of (A,�,w). In 1978, Salomaa and Soittola deduced the following result from their thorough study of the theory of ra- tional power series: if the D0L-sequence generated by (A,�,w) is not eventually the empty word then there exist an integer � ≥ 0 and a real number � ≥ 1 such that |�n(w)| behaves like nα�n as n tends to infinity. The aim of the present paper is to present a short, direct, elementary proof of this theorem. |
Year | Venue | Keywords |
|---|---|---|
2008 | Clinical Orthopaedics and Related Research | discrete mathematics,power series |
Field | DocType | Volume |
Integer,Discrete mathematics,Combinatorics,Elementary proof,Free monoid,Asymptotic analysis,Power series,Real number,Mathematics,Alphabet,Endomorphism | Journal | abs/0804.1 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Julien Cassaigne | 1 | 282 | 40.80 |
| Christian Mauduit | 2 | 41 | 8.90 |
| François Nicolas | 3 | 5 | 2.48 |