Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Binary codes and partial permutation decoding sets from the odd graphs

100%

Fish W., Fray R., Mwambene E.

Open Mathematics

2014

tom 12

nr 9

1362-1371

For k ≥ 1, the odd graph denoted by O(k), is the graph with the vertex-set Ω{k}, the set of all k-subsets of Ω = {1, 2, …, 2k +1}, and any two of its vertices u and v constitute an edge [u, v] if and only if u ∩ v = /0. In this paper the binary code generated by the adjacency matrix of O(k) is studied. The automorphism group of the code is determined, and by identifying a suitable information set, a 2-PD-set of the order of k 4 is determined. Lastly, the relationship between the dual code from O(k) and the code from its graph-theoretical complement $\overline {O(k)} $, is investigated.

The subalgebra lattice of a finite algebra

72%

Pióro K.

Open Mathematics

2014

tom 12

nr 7

1052-1108

The aim of this paper is to characterize pairs (L, A), where L is a finite lattice and A a finite algebra, such that the subalgebra lattice of A is isomorphic to L. Next, necessary and sufficient conditions are found for pairs of finite algebras (of possibly distinct types) to have isomorphic subalgebra lattices. Both of these characterizations are particularly simple in the case of distributive subalgebra lattices. We do not restrict our attention to total algebras only, but we consider the more general case of partial algebras. Moreover, we use connections between algebras and hypergraphs to solve these problems.

Ograniczanie wyników

2 Open Mathematics

1 Fish W.

1 Fray R.

1 Mwambene E.

1 Pióro K.

2 2014

Wyniki wyszukiwania

Binary codes and partial permutation decoding sets from the odd graphs

The subalgebra lattice of a finite algebra