Atoms and partial orders of infinite languages
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 35 (2001) no. 4, pp. 389-401.

We determine minimal elements, i.e., atoms, in certain partial orders of factor closed languages under $\subseteq$. This is in analogy to structural Ramsey theory which determines minimal structures in partial orders under embedding.

Classification: 68R15,  05C55
Keywords: combinatorics of words, structural Ramsey theory
@article{ITA_2001__35_4_389_0,
author = {Kuich, Werner and Sauer, N. W.},
title = {Atoms and partial orders of infinite languages},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {389--401},
publisher = {EDP-Sciences},
volume = {35},
number = {4},
year = {2001},
zbl = {1112.68435},
mrnumber = {1880807},
language = {en},
url = {http://www.numdam.org/item/ITA_2001__35_4_389_0/}
}
TY  - JOUR
AU  - Kuich, Werner
AU  - Sauer, N. W.
TI  - Atoms and partial orders of infinite languages
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2001
DA  - 2001///
SP  - 389
EP  - 401
VL  - 35
IS  - 4
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/ITA_2001__35_4_389_0/
UR  - https://zbmath.org/?q=an%3A1112.68435
UR  - https://www.ams.org/mathscinet-getitem?mr=1880807
LA  - en
ID  - ITA_2001__35_4_389_0
ER  -
%0 Journal Article
%A Kuich, Werner
%A Sauer, N. W.
%T Atoms and partial orders of infinite languages
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2001
%P 389-401
%V 35
%N 4
%I EDP-Sciences
%G en
%F ITA_2001__35_4_389_0
Kuich, Werner; Sauer, N. W. Atoms and partial orders of infinite languages. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 35 (2001) no. 4, pp. 389-401. http://www.numdam.org/item/ITA_2001__35_4_389_0/

[1] A. De Luca and St. Varrichio, Finiteness and Regularity in Semigroups and Formal Languages. Springer (1999). | MR | Zbl

[2] H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton University Press, Princeton (1981). | MR | Zbl

[3] M. Pouzet and N. Sauer, Edge partitions of the Rado graph. Combinatorica 16 (1996) 1-16. | MR | Zbl

[4] F.P. Ramsey, On a problem of formal logic. Proc. London Math. Soc. 30 (1930) 264-286. | JFM

[5] N. Sauer, Coloring finite substructures of countable structures. The Mathematics of Paul Erdős, X. Bolyai Mathematical Society (to appear). | MR | Zbl

[6] S. Yu, Regular Languages. In: Handbook of Formal Languages, edited by G. Rozenberg and A. Salomaa, Springer (1997). | MR