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Disjoint sequences in Boolean algebras

Ján Jakubík (1998)

Mathematica Bohemica

We deal with the system Conv B of all sequential convergences on a Boolean algebra B . We prove that if α is a sequential convergence on B which is generated by a set of disjoint sequences and if β is any element of Conv B , then the join α β exists in the partially ordered set Conv B . Further we show that each interval of Conv B is a Brouwerian lattice.

F-Normalreihen.

Herbert Möller (1977)

Journal für die reine und angewandte Mathematik

Increasing integer sequences and Goldbach's conjecture

Mauro Torelli (2006)

RAIRO - Theoretical Informatics and Applications

Increasing integer sequences include many instances of interesting sequences and combinatorial structures, ranging from tournaments to addition chains, from permutations to sequences having the Goldbach property that any integer greater than 1 can be obtained as the sum of two elements in the sequence. The paper introduces and compares several of these classes of sequences, discussing recurrence relations, enumerative problems and questions concerning shortest sequences.

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