Minimizing bumps in linear extensions of ordered sets

A linear extension x ₁ x ₂ x ₃ ... of a partially ordered set (X, <) has a bump whenever x _i <x _i +1. We examine the problem of determining linear extensions with as few bumps as possible. Heuristic algorithms for approximate bump minimization are considered.     

Linear expanded xanthines

Expansion of the xanthine ring system has been accomplished by linear formation of a benzo, pyrido or pyrazino ring between the pyrimidine and imidazole portions.

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Linear expandierte Xanthine (Kurze Mitteilung)

Zusammenfassung Durch Einbau eines Benzo-, Pyrido- oder Pyrazino-Ringes zwischen den Pyrimidin- und Imidazoleinheiten wurde die lineare Expansion des Xanthin-Ringsystems erreicht.

     

A property of the lattice of equational theories

It had been conjectured that any algebraic lattice having a compact one could be represented as the lattice of equational theories extending some theory. However, we show that each lattice having such a representation satisfies a nontrivial quasidistributivity condition. In particular,M ₃ has no such representation.To the memory of András HuhnPresented by Walter Taylor.     

Blei

Ohne Zusammenfassung