منابع مشابه
Combinatorial Grassmannians
We follow the rules: k, n denote elements of N and X, Y , Z denote sets. One can prove the following propositions: (1) For all sets a, b such that a 6= b and a = n and b = n holds a ∩ b < n and n+ 1 ≤ a ∪ b. (2) For all sets a, b such that a = n+ k and b = n+ k holds a ∩ b = n iff a ∪ b = n+ 2 · k. (3) X ≤ Y iff there exists a function f such that f is one-to-one and X ⊆ dom f and f ◦X ⊆ Y. (4)...
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Oriented matroids have long been of use in various areas of combinatorics [BLS93]. Gelfand and MacPherson [GM92] initiated the use of oriented matroids in manifold and bundle theory, using them to formulate a combinatorial formula for the rational Pontrjagin classes of a differentiable manifold. MacPherson [Mac93] abstracted this into a manifold theory (combinatorial differential (CD) manifolds...
متن کاملCombinatorial Models for the Finite-Dimensional Grassmannians
Let Mn be a linear hyperplane arrangement in IR. We define finite posets Gk(M) and Vk(M) of oriented matroids associated with this, which approximate the Grassmannian Gk(IR) and the Stiefel manifold Vk(IR), respectively. The basic conjectures are that the “OM-Grassmannian” Gk(M) has the homotopy type of Gk(IR), and that the “OM-Stiefel bundle” ∆π : ∆Vk(M) −→ ∆Gk(M) is a surjective map. These co...
متن کاملWeighted Grassmannians
Many classes of projective algebraic varieties can be studied in terms of graded rings. Gorenstein graded rings in small codimension have been studied recently from an algebraic point of view, but the geometric meaning of the resulting structures is still relatively poorly understood. We discuss here the weighted projective analogs of homogeneous spaces such as the Grassmannian Gr(2, 5) and ort...
متن کاملUnitary Grassmannians
We study projective homogeneous varieties under an action of a projective unitary group (of outer type). We are especially interested in the case of (unitary) grassmannians of totally isotropic subspaces of a hermitian form over a field, the main result saying that these grassmannians are 2-incompressible if the hermitian form is generic. Applications to orthogonal grassmannians are provided.
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2007
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-007-0004-9