Two partial orders on the set of antichains

J. Crampton; G. Loizou

Two partial orders on the set of antichains

Research output: Working paper

Abstract

Given a poset $X$, we define two partial orders on the set of antichains of $X$. We prove that the two resulting posets $langle A(X) preccurlyeq and $langle A(X) preccurlyeq' are lattices which are isomorphic to the lattice of order ideals of $X$, $langle I(X) subseteq . We also establish the meet and join operations of the two resulting lattices.

Original language	English
Publication status	Published - 2000

Cite this

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title = "Two partial orders on the set of antichains",

abstract = "Given a poset $X$, we define two partial orders on the set of antichains of $X$. We prove that the two resulting posets $langle A(X) preccurlyeq and $langle A(X) preccurlyeq' are lattices which are isomorphic to the lattice of order ideals of $X$, $langle I(X) subseteq . We also establish the meet and join operations of the two resulting lattices.",

author = "J. Crampton and G. Loizou",

year = "2000",

language = "English",

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T1 - Two partial orders on the set of antichains

AU - Crampton, J.

AU - Loizou, G.

PY - 2000

Y1 - 2000

N2 - Given a poset $X$, we define two partial orders on the set of antichains of $X$. We prove that the two resulting posets $langle A(X) preccurlyeq and $langle A(X) preccurlyeq' are lattices which are isomorphic to the lattice of order ideals of $X$, $langle I(X) subseteq . We also establish the meet and join operations of the two resulting lattices.

AB - Given a poset $X$, we define two partial orders on the set of antichains of $X$. We prove that the two resulting posets $langle A(X) preccurlyeq and $langle A(X) preccurlyeq' are lattices which are isomorphic to the lattice of order ideals of $X$, $langle I(X) subseteq . We also establish the meet and join operations of the two resulting lattices.

M3 - Working paper

BT - Two partial orders on the set of antichains

ER -