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

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 39, Issue: 1, page 305-322
- ISSN: 0988-3754

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topÉsik, Zoltán, and Németh, Zoltán L.. "Algebraic and graph-theoretic properties of infinite n-posets." RAIRO - Theoretical Informatics and Applications 39.1 (2010): 305-322. <http://eudml.org/doc/92763>.

@article{Ésik2010,

abstract = {
A Σ-labeled n-poset is an (at most) countable set,
labeled in the set Σ, equipped with n partial orders.
The collection of all Σ-labeled n-posets is naturally
equipped with n binary product operations and
nω-ary product operations.
Moreover, the ω-ary product operations
give rise to nω-power operations.
We show that those Σ-labeled n-posets that can be generated from
the singletons by the binary and ω-ary
product operations form the free algebra on Σ
in a variety axiomatizable by an infinite collection of simple
equations. When n = 1, this variety coincides with the class of
ω-semigroups of Perrin and Pin.
Moreover, we show that those Σ-labeled
n-posets that can be generated from
the singletons by the binary product operations and
the ω-power operations form the free algebra on Σ
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},

keywords = {Poset; n-poset; composition; free algebra; equational logic},

language = {eng},

month = {3},

number = {1},

pages = {305-322},

publisher = {EDP Sciences},

title = {Algebraic and graph-theoretic properties of infinite n-posets},

url = {http://eudml.org/doc/92763},

volume = {39},

year = {2010},

}

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

DA - 2010/3//

PB - EDP Sciences

VL - 39

IS - 1

SP - 305

EP - 322

AB -
A Σ-labeled n-poset is an (at most) countable set,
labeled in the set Σ, equipped with n partial orders.
The collection of all Σ-labeled n-posets is naturally
equipped with n binary product operations and
nω-ary product operations.
Moreover, the ω-ary product operations
give rise to nω-power operations.
We show that those Σ-labeled n-posets that can be generated from
the singletons by the binary and ω-ary
product operations form the free algebra on Σ
in a variety axiomatizable by an infinite collection of simple
equations. When n = 1, this variety coincides with the class of
ω-semigroups of Perrin and Pin.
Moreover, we show that those Σ-labeled
n-posets that can be generated from
the singletons by the binary product operations and
the ω-power operations form the free algebra on Σ
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/92763

ER -

## References

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