Displaying similar documents to “On monotone permutations of ℓ -cyclically ordered sets”

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 ) + ∑ x ∈ P s ( Q x ) , where s ( X ) denotes the jump number of an ordered set X . We first show that w ( P ) - 1 + ∑ x ∈ P s ( Q x ) ≤ s ( Q ) ≤ s ( P ) + ∑ x ∈ 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...

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 ∈ 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 ∈ A there exist a minimal element u and a maximal element v with u ≤ a ≤ 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.