Matching Tag: real-schubert-calculus
Let V ∈ Gr k , n ( R ) V\in\operatorname{Gr}_{k,n}(\mathbb{R}) V ∈ Gr k , n ( R ) Wr ( V ) \operatorname{Wr}(V) Wr ( V ) I ⊆ R I\subseteq\mathbb{R} I ⊆ R
Let α = { α 1 < ⋯ < α k } \alpha=\{\alpha_1<\dotsb<\alpha_k\} α = { α 1 < ⋯ < α k } α k < n \alpha_k<n α k < n ( w 1 , … , w m ) (w_1,\dotsc,w_m) ( w 1 , … , w m ) F ℓ ( α ; n ) \mathbb{F}\ell(\alpha;n) F ℓ ( α ; n ) w i w_i w i
Let m , p > 1 m,p>1 m , p > 1 Grass ( p , m + p ) \operatorname{Grass}(p,m+p) Grass ( p , m + p ) α 1 , … , α n \alpha^1,\ldots,\alpha^n α 1 , … , α n 1 1 1
Let γ \gamma γ S i = { s i 1 , … , s i n } S_i=\{s_{i1},\dotsc,s_{in}\} S i = { s i 1 , … , s in } n n n R P 1 \mathbb{R}\mathbb{P}^1 R P 1 F ∙ ( S i ) F_\bullet(S_i) F ∙ ( S i )
Let ( w 1 , … , w m ) (w_1,\dotsc,w_m) ( w 1 , … , w m ) F ℓ ( α ; n ) \mathbb{F}\ell(\alpha;n) F ℓ ( α ; n ) δ ( w i ) \delta(w_i) δ ( w i ) w i w_i w i Δ w ( t 1 , … , t m ) \Delta_w(t_1,\dotsc,t_m) Δ w ( t 1 , … , t m )
Let α = { α 1 < ⋯ < α k } \alpha=\{\alpha_1<\dotsb<\alpha_k\} α = { α 1 < ⋯ < α k } α k < n \alpha_k<n α k < n ( w 1 , … , w m ) (w_1,\dotsc,w_m) ( w 1 , … , w m ) F ℓ ( α ; n ) \mathbb{F}\ell(\alpha;n) F ℓ ( α ; n )
Let a = ( a 1 < ⋯ < a k ) a=(a_1<\dotsb<a_k) a = ( a 1 < ⋯ < a k ) n n n a k < n a_k<n a k < n W a W^a W a F ℓ ( a ; n ) \mathbb F\ell(a;n) F ℓ ( a ; n ) w 1 , … , w m ∈ W a w_1,\dotsc,w_m\in W^a w 1 , … , w m ∈ W a
Let γ : R → R m − 1 [ u ] \gamma:\mathbb{R}\to\mathbb{R}_{m-1}[u] γ : R → R m − 1 [ u ] m m m γ \gamma γ z 1 , … , z d ( m − d ) z_1,\dots,z_{d(m-d)} z 1 , … , z d ( m − d )
Let ν ⊢ n \nu\vdash n ν ⊢ n μ ⊩ κ \boldsymbol{\mu}\Vdash\kappa μ ⊩ κ κ = ( κ 1 , … , κ s ) \kappa=(\kappa_1,\dots,\kappa_s) κ = ( κ 1 , … , κ s ) n n n I 1 , … , I s ⊆ R I_1,\dots,I_s\subseteq\mathbb{R} I 1 , … , I s ⊆ R
Let 0 ≤ k ≤ n 0\le k\le n 0 ≤ k ≤ n I 1 , … , I k ( n − k ) I_1,\dots,I_{k(n-k)} I 1 , … , I k ( n − k ) P 1 ( R ) \mathbb{P}^1(\mathbb{R}) P 1 ( R ) l l l X l X_l X l k k k I l I_l I l
Consider a real Schubert problem for which Proposition … is sharp. The conjecture asserts that the cohomological lower bound can always be attained; the supplied excerpt gives no r…
Monotone Osculating Conjecture. For any such Schubert problem and any flags F ∙ 1 , … , F ∙ m F_{\bullet}^1,\ldots,F_{\bullet}^m F ∙ 1 , … , F ∙ m γ \gamma γ
Monotone Secant Conjecture. For any Grassmannian Schubert problem ( σ 1 , … , σ m ) (\sigma_1,\ldots, \sigma_m) ( σ 1 , … , σ m ) F ℓ ( α ; n ) \mathbb{F}\ell(\alpha;n) F ℓ ( α ; n )
Let G ( k , n ) G(k,n) G ( k , n ) γ \gamma γ λ 1 , … , λ m \lambda^1,\dotsc,\lambda^m λ 1 , … , λ m G ( k , n ) G(k,n) G ( k , n )
