title: On possible dimensions of subspace intersections
metadata.name: dc.contributor.author
metadata.value: Lebedinskaya, Natalia A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Lebedinskii, Dmitrii M.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-08-01T10:38:18Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-08-01T10:38:18Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-06
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/2456
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We consider the problem concerning the dimensions of the intersections of a subspace in the direct sum of
  a finite series of finite-dimensional vector spaces with the sums of pairs of direct summands, provided that
  the subspace intersection with each of these direct summands is zero. The problem is naturally divided in
  two: Find conditions for the existence and for the representability of the corresponding matroid. In the paper, we give necessary and sufficient conditions of the existence of a matroid if some ranks of subsets
  of the base set are known. Using these conditions, we also present necessary conditions of the existence
  of a matroid with base set composed of a finite series of disjoint sets of full rank and the ranks of their
  pairwise unions are given. A simple graphical representation of the latter conditions is given as well. These
  conditions are also necessary for the subspace to exist. At the end of the paper, we state a conjecture that
  these conditions are sufficient as well. Refs 4. Figs 3.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Series 1. Mathematics. Mechanics. Astronomy;Vol. 3 (61); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: direct sum
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: subspace
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: matroid
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On possible dimensions of subspace intersections
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: Лебединская_Лебединский.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/2456/1/%d0%9b%d0%b5%d0%b1%d0%b5%d0%b4%d0%b8%d0%bd%d1%81%d0%ba%d0%b0%d1%8f_%d0%9b%d0%b5%d0%b1%d0%b5%d0%b4%d0%b8%d0%bd%d1%81%d0%ba%d0%b8%d0%b9.pdf
resources.format: Adobe PDF
resources.size: 216,36 kB