Characterization of posets of intervals

Judita Lihová

Displaying similar documents to “Characterization of posets of intervals”

On the jump number of lexicographic sums of ordered sets

Hyung Chan Jung, Jeh Gwon Lee (2003)

Czechoslovak Mathematical Journal

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Let $Q$ be the lexicographic sum of finite ordered sets $Q_{x}$ over a finite ordered set $P$ . For some $P$ we can give a formula for the jump number of $Q$ in terms of the jump numbers of $Q_{x}$ and $P$ , that is, $s (Q) = s (P) + \sum_{x \in P} s (Q_{x})$ , where $s (X)$ denotes the jump number of an ordered set $X$ . We first show that $w (P) - 1 + \sum_{x \in P} s (Q_{x}) \leq s (Q) \leq s (P) + \sum_{x \in P} s (Q_{x})$ , where $w (X)$ denotes the width of an ordered set $X$ . Consequently, if $P$ is a Dilworth ordered set, that is, $s (P) = w (P) - 1$ , then the formula holds. We also show that it holds again if $P$ is bipartite. Finally, we prove that the lexicographic...

Orthomodular lattices and closure operations in ordered vector spaces

Jan Florek (2010)

Banach Center Publications

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On a non-trivial partially ordered real vector space (V,≤) the orthogonality relation is defined by incomparability and ζ(V,⊥) is a complete lattice of double orthoclosed sets. We say that A ⊆ V is an orthogonal set when for all a,b ∈ A with a ≠ b, we have a ⊥ b. In our earlier papers we defined an integrally open ordered vector space and two closure operations A → D(A) and $A \to A^{⊥ ⊥}$ . It was proved that V is integrally open iff $D (A) = A^{⊥ ⊥}$ for every orthogonal set A ⊆ V. In this paper we generalize this...

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.

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 “Characterization of posets of intervals”

On the jump number of lexicographic sums of ordered sets

Orthomodular lattices and closure operations in ordered vector spaces

On monotone permutations of ℓ -cyclically ordered sets

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

On monotone permutations of $ℓ$ -cyclically ordered sets