On the jump number of lexicographic sums of ordered sets

Hyung Chan Jung; Jeh Gwon Lee

Displaying similar documents to “On the jump number of lexicographic sums of ordered sets”

On monotone permutations of $ℓ$ -cyclically ordered sets

Ján Jakubík (2006)

Czechoslovak Mathematical Journal

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For an $ℓ$ -cyclically ordered set $M$ with the $ℓ$ -cyclic order $C$ let $P (M)$ be the set of all monotone permutations on $M$ . We define a ternary relation $\bar{C}$ on the set $P (M)$ . Further, we define in a natural way a group operation (denoted by $\cdot$ ) on $P (M)$ . We prove that if the $ℓ$ -cyclic order $C$ is complete and $\bar{C} \neq \emptyset$ , then $(P (M), \cdot, \bar{C})$ is a half cyclically ordered group.

Characterization of posets of intervals

Judita Lihová (2000)

Archivum Mathematicum

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If $A$ is a class of partially ordered sets, let $P (A)$ denote the system of all posets which are isomorphic to the system of all intervals of $A$ for some $A \in A .$ We give an algebraic characterization of elements of $P (A)$ for $A$ being the class of all bounded posets and the class of all posets $A$ satisfying the condition that for each $a \in A$ there exist a minimal element $u$ and a maximal element $v$ with $u \leq a \leq v,$ respectively.

Selfduality of the system of convex subsets of a partially ordered set

Miron Zelina (1993)

Commentationes Mathematicae Universitatis Carolinae

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For a partially ordered set $P$ let us denote by $C o P$ the system of all convex subsets of $P$ . It is found the necessary and sufficient condition (concerning $P$ ) under which $C o P$ (as a partially ordered set) is selfdual.

Displaying similar documents to “On the jump number of lexicographic sums of ordered sets”

On monotone permutations of ℓ -cyclically ordered sets

Characterization of posets of intervals

Selfduality of the system of convex subsets of a partially ordered set

On monotone permutations of $ℓ$ -cyclically ordered sets