Algebraic and graph-theoretic properties of infinite $n$-posets

Ésik, Zoltán, and Németh, Zoltán L.. "Algebraic and graph-theoretic properties of infinite $n$-posets." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 39.1 (2005): 305-322. <http://eudml.org/doc/246097>.

@article{Ésik2005,
abstract = {A $\Sigma $-labeled $n$-poset is an (at most) countable set, labeled in the set $\Sigma $, equipped with $n$ partial orders. The collection of all $\Sigma $-labeled $n$-posets is naturally equipped with $n$ binary product operations and $n$$\omega $-ary product operations. Moreover, the $\omega $-ary product operations give rise to $n$$\omega $-power operations. We show that those $\Sigma $-labeled $n$-posets that can be generated from the singletons by the binary and $\omega $-ary product operations form the free algebra on $\Sigma $ in a variety axiomatizable by an infinite collection of simple equations. When $n = 1$, this variety coincides with the class of $\omega $-semigroups of Perrin and Pin. Moreover, we show that those $\Sigma $-labeled $n$-posets that can be generated from the singletons by the binary product operations and the $\omega $-power operations form the free algebra on $\Sigma $ in a related variety that generalizes Wilke’s algebras. We also give graph-theoretic characterizations of those $n$-posets contained in the above free algebras. Our results serve as a preliminary study to a development of a theory of higher dimensional automata and languages on infinitary associative structures.},
author = {Ésik, Zoltán, Németh, Zoltán L.},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {poset; $n$-poset; composition; free algebra; equational logic},
language = {eng},
number = {1},
pages = {305-322},
publisher = {EDP-Sciences},
title = {Algebraic and graph-theoretic properties of infinite $n$-posets},
url = {http://eudml.org/doc/246097},
volume = {39},
year = {2005},
}

TY - JOUR
AU - Ésik, Zoltán
AU - Németh, Zoltán L.
TI - Algebraic and graph-theoretic properties of infinite $n$-posets
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2005
PB - EDP-Sciences
VL - 39
IS - 1
SP - 305
EP - 322
AB - A $\Sigma $-labeled $n$-poset is an (at most) countable set, labeled in the set $\Sigma $, equipped with $n$ partial orders. The collection of all $\Sigma $-labeled $n$-posets is naturally equipped with $n$ binary product operations and $n$$\omega $-ary product operations. Moreover, the $\omega $-ary product operations give rise to $n$$\omega $-power operations. We show that those $\Sigma $-labeled $n$-posets that can be generated from the singletons by the binary and $\omega $-ary product operations form the free algebra on $\Sigma $ in a variety axiomatizable by an infinite collection of simple equations. When $n = 1$, this variety coincides with the class of $\omega $-semigroups of Perrin and Pin. Moreover, we show that those $\Sigma $-labeled $n$-posets that can be generated from the singletons by the binary product operations and the $\omega $-power operations form the free algebra on $\Sigma $ in a related variety that generalizes Wilke’s algebras. We also give graph-theoretic characterizations of those $n$-posets contained in the above free algebras. Our results serve as a preliminary study to a development of a theory of higher dimensional automata and languages on infinitary associative structures.
LA - eng
KW - poset; $n$-poset; composition; free algebra; equational logic
UR - http://eudml.org/doc/246097
ER -