Geodesic
Possible dimensions of subspace intersections for five direct summands
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIX, Tome 453 (2016), pp. 189-197
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The paper consides the problem on 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 empty. The problem is naturally divided into two ones: Find conditions for the existence and for the representability of the corresponding matroid. The following theorem is proved: If the ranks of all the unions of a series of blocks satisfying the condition for the ranks of subsets in the matroid are given and the blocks have full rank, then this partial rank function can be extended to a full rank function for all the subsets of the base set (the union of all the blocks). Necessary and sufficient conditions on the dimensions of the direct summands and intersections mentioned above for the corresponding matroid to exist are obtained in the case of five direct summands. 
@article{ZNSL_2016_453_a12,
     author = {N. A. Lebedinskaya and D. M. Lebedinskii and A. A. Smirnov},
     title = {Possible dimensions of subspace intersections for five direct summands},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {189--197},
     year = {2016},
     volume = {453},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_453_a12/}
}
TY  - JOUR
AU  - N. A. Lebedinskaya
AU  - D. M. Lebedinskii
AU  - A. A. Smirnov
TI  - Possible dimensions of subspace intersections for five direct summands
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2016
SP  - 189
EP  - 197
VL  - 453
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2016_453_a12/
LA  - ru
ID  - ZNSL_2016_453_a12
ER  - 
%0 Journal Article
%A N. A. Lebedinskaya
%A D. M. Lebedinskii
%A A. A. Smirnov
%T Possible dimensions of subspace intersections for five direct summands
%J Zapiski Nauchnykh Seminarov POMI
%D 2016
%P 189-197
%V 453
%U http://geodesic.mathdoc.fr/item/ZNSL_2016_453_a12/
%G ru
%F ZNSL_2016_453_a12
N. A. Lebedinskaya; D. M. Lebedinskii; A. A. Smirnov. Possible dimensions of subspace intersections for five direct summands. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIX, Tome 453 (2016), pp. 189-197. http://geodesic.mathdoc.fr/item/ZNSL_2016_453_a12/

[1] J. G. Oxley, “What is a matroid?”, Cubo, 5 (2003), 179–218 | MR | Zbl

[2] M. M. Shikare, B. N. Waphare, Combinatorial Optimization, Narosa Publishing House, 2004

[3] N. A. Lebedinskaya, D. M. Lebedinskii, “O vozmozhnykh znacheniyakh razmernostei peresechenii podprostranstv”, Vestnik SPBGU, Ser. 1 matematika, mekhanika, astronomiya, 2016, no. 2, 204–209

[4] 4ti2 team. 4ti2 – A software package for algebraic, geometric and combinatorial problems on linear spaces, Available at http://www.4ti2.de

[5] J. Ellson, E. Gansner, L. Koutsofios, S. North, G. Woodhull, “Graphviz – open source graph drawing tools”, Lect. Notes Comput. Sci., 2265, Springer-Verlag, 2001, 483–484 | DOI