Аннотация:
The main goal of the presented study is to develop methods for working with multidimensional matrices that can be applied to problems of existence and enumeration of various structures in hypergraphs. Many results in the search for substructures in graphs are based on certain correspondences between graphs and matrices and the application of linear algebra methods. Among the most important topics in the combinatorial matrix theory are the representation of graphs using adjacency and incidence matrices, the Konig-Hall theorem for systems of distinct representatives, the permanents of doubly stochastic matrices, and Latin squares. We generalize these directions to multidimensional matrices and hypergraphs and lay the foundations of the combinatorial theory of multidimensional matrices.
Язык доклада: английский
Website:
https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pnQT09
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