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- W2522682047 abstract "A new algebraic structure is described, that is a useful framework in which reconstruction problems and results can be expressed. A conjecture is made which would, provided it is true, help to address the problem of symmetries. A consequence of the abstract language in which the theory is formulated is the expression of relations between the numbers of substructures of a structure (for example, the number of subgraphs of a given isomorphism class in a graph). Moreover, a generalisation similar to the one achieved by P.J.Cameron and V.B.Mnukhin of the results of edge reconstruction to invariant algebras apply in this new structure. Examples are provided to show that the result of L.Lovasz is best possible if one knows nothing about the underlying group, and that the result of V.Muller is best possible if one knows only the order of the group. Thus, reconstruction problems are set in a theory that generates relations to address them, and at the same time, provides examples establishing the sharpness of the theorems." @default.
- W2522682047 created "2016-09-30" @default.
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- W2522682047 date "2010-04-14" @default.
- W2522682047 modified "2023-09-27" @default.
- W2522682047 title "On some algebraic and combinatorial properties of the number of substructures" @default.
- W2522682047 hasPublicationYear "2010" @default.
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