Standard

Combinatorial models for the finite-dimensional Grassmannians. / Mnëv, Nicolai E.; Ziegler, Günter M.

в: Discrete and Computational Geometry, Том 10, № 1, 01.12.1993, стр. 241-250.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Mnëv, NE & Ziegler, GM 1993, 'Combinatorial models for the finite-dimensional Grassmannians', Discrete and Computational Geometry, Том. 10, № 1, стр. 241-250. https://doi.org/10.1007/BF02573979

APA

Mnëv, N. E., & Ziegler, G. M. (1993). Combinatorial models for the finite-dimensional Grassmannians. Discrete and Computational Geometry, 10(1), 241-250. https://doi.org/10.1007/BF02573979

Vancouver

Mnëv NE, Ziegler GM. Combinatorial models for the finite-dimensional Grassmannians. Discrete and Computational Geometry. 1993 Дек. 1;10(1):241-250. https://doi.org/10.1007/BF02573979

Author

Mnëv, Nicolai E. ; Ziegler, Günter M. / Combinatorial models for the finite-dimensional Grassmannians. в: Discrete and Computational Geometry. 1993 ; Том 10, № 1. стр. 241-250.

BibTeX

@article{39412284da924b7eba2619c5bbadf0cd,
title = "Combinatorial models for the finite-dimensional Grassmannians",
abstract = "Let ℳ n be a linear hyperplane arrangement in ℝ n . We define two corresponding posets G k (ℳ n and V k (ℳ n ) of oriented matroids, which approximate the Grassmannian G k (ℝ n ) and the Stiefel manifold V k (ℝ n ). The basic conjectures are that the {"}OM-Grassmannian{"}G k (ℳ n ) has the homotopy type of G k (ℝ n ), and that the {"}OM-Stiefel bundle{"} Δπ: ΔV k (ℳ n ) → ΔG k (ℳ n ) is a surjective map. These conjectures can be proved in some cases: we survey the known results and add some new ones. The conjectures fail if they are generalized to nonrealizable oriented matroids ℳ n . {\textcopyright} 1993 Springer-Verlag New York Inc.",
author = "Mn{\"e}v, {Nicolai E.} and Ziegler, {G{\"u}nter M.}",
year = "1993",
month = dec,
day = "1",
doi = "10.1007/BF02573979",
language = "English",
volume = "10",
pages = "241--250",
journal = "Discrete and Computational Geometry",
issn = "0179-5376",
publisher = "Springer Nature",
number = "1",

}

RIS

TY - JOUR

T1 - Combinatorial models for the finite-dimensional Grassmannians

AU - Mnëv, Nicolai E.

AU - Ziegler, Günter M.

PY - 1993/12/1

Y1 - 1993/12/1

N2 - Let ℳ n be a linear hyperplane arrangement in ℝ n . We define two corresponding posets G k (ℳ n and V k (ℳ n ) of oriented matroids, which approximate the Grassmannian G k (ℝ n ) and the Stiefel manifold V k (ℝ n ). The basic conjectures are that the "OM-Grassmannian"G k (ℳ n ) has the homotopy type of G k (ℝ n ), and that the "OM-Stiefel bundle" Δπ: ΔV k (ℳ n ) → ΔG k (ℳ n ) is a surjective map. These conjectures can be proved in some cases: we survey the known results and add some new ones. The conjectures fail if they are generalized to nonrealizable oriented matroids ℳ n . © 1993 Springer-Verlag New York Inc.

AB - Let ℳ n be a linear hyperplane arrangement in ℝ n . We define two corresponding posets G k (ℳ n and V k (ℳ n ) of oriented matroids, which approximate the Grassmannian G k (ℝ n ) and the Stiefel manifold V k (ℝ n ). The basic conjectures are that the "OM-Grassmannian"G k (ℳ n ) has the homotopy type of G k (ℝ n ), and that the "OM-Stiefel bundle" Δπ: ΔV k (ℳ n ) → ΔG k (ℳ n ) is a surjective map. These conjectures can be proved in some cases: we survey the known results and add some new ones. The conjectures fail if they are generalized to nonrealizable oriented matroids ℳ n . © 1993 Springer-Verlag New York Inc.

UR - http://www.scopus.com/inward/record.url?scp=51249170102&partnerID=8YFLogxK

U2 - 10.1007/BF02573979

DO - 10.1007/BF02573979

M3 - Article

AN - SCOPUS:51249170102

VL - 10

SP - 241

EP - 250

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 1

ER -

ID: 126277496