Geodesic
On homogeneous matroids corresponding to block-schemes
Prikladnaya Diskretnaya Matematika. Supplement, no. 13 (2020), pp. 8-12

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The paper deals with relationship of homogeneous matroids and block-schemes. This problem is related to the study of access structures of ideal perfect secrets sharing schemes. By homogeneous matroids we mean an equal degree of cycles, where, perhaps, not all subsets of this degree are cycles. If power of cycles is equal to five, then it is proved that homogeneous connected separating matroid will be uniform. However, if the matroid is connected and separating, then the dual matroid will be simple. It is proved that if each cycle of homogeneous separating connected matroid is a hyperplane, then a block-scheme corresponds to it.
Keywords: homogeneous matroids, secret sharing schemes, block-schemes
Mots-clés : cycles. 
@article{PDMA_2020_13_a1,
     author = {N. V. Medvedev and S. S. Titov},
     title = {On homogeneous matroids corresponding to block-schemes},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {8--12},
     publisher = {mathdoc},
     number = {13},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2020_13_a1/}
}
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N. V. Medvedev; S. S. Titov. On homogeneous matroids corresponding to block-schemes. Prikladnaya Diskretnaya Matematika. Supplement, no. 13 (2020), pp. 8-12. http://geodesic.mathdoc.fr/item/PDMA_2020_13_a1/