Báo cáo toán học: "Finite vector spaces and certain lattices" pps

... the pair of lattices which are solution spaces of Bx ≡ 0modrand Cx ≡ 0mods, (5) where the matrices B and C are defined by A ≡ B mod r and A ≡ C mod s;(6) and conversely, given (5) we define a matrix ... number of r-dimensional vector subspaces of the n-dimensional vector space V n (q) over the finite field GF (q). We let G n = G n (q) denote the total number of vector subspaces of V...

Ngày tải lên: 07/08/2014, 06:22

Ngày tải lên: 05/08/2014, 15:21

... ≥ 0. Then n = 4and λ =(2 2 ), n = 6and λ =(3, 2, 1) or n = 8and λ =(3, 2, 1 3 ). Proof. By Lemma 4.4(1) , k ≤ 3, and by (A1), n − k − 2 ≥ k + 2, hence n ≥ 2k +4. Here, µ =(k +1, 1) and π 1 = n. If ... λ 1 = l and λ 2 =1, and hence λ is a hook partition. Proof. (1) and (2) are trivial. Part (3) follows from the fact that exactly k +1 rim nodes of the (1,1)-hook of µ are in the firs...

Ngày tải lên: 07/08/2014, 08:22

... bottom left and upper right corners of the skew shape (n kn )/((n − 1) k , . . . , 2 k , 1 k ) at (1, 0) and (n + 1, kn) in Z 2 , respectively, and add the two line segments (0, 0) → (1, 0) and (n ... background is put in Section 2 and we will see that this work is a generalization of Haiman’s and Stanley’s results. In Sections 3 and 4 we prove the Fuss type A and Fuss type B...

Ngày tải lên: 07/08/2014, 21:21

... about W (v) and A(v) is given in the following lemma and its corollary. Lemma 2.4. If two vertices v and v ′ have sequences of colors that agree thro ugh w l−1 , then the order of v and v ′ is ... hypothesis v and v ′ come in the same order as (−1) r l (v) w l (v) and (−1) r l (v ′ ) w l (v ′ ) since w l (v) and w l (v ′ ) have the same color. By taking the case l = 1 applied to...

Ngày tải lên: 08/08/2014, 11:20

... subset A and B such that the induced graphs G[A] and G[B] are edge-empty and complete, respectively, and, thus, we have a contradiction by Proposition 5.1. Suppose |S|  4, and let H 1 and H 2 denote disjoint ... h r and t must have at least one non-neighbour in B(xs), and, since r and t are adjacent, it follows that r and t must have distinct non-neighbours, say q and u,...

Ngày tải lên: 08/08/2014, 12:22

... Suppose m ∈ and σ>0 are constants with a <m ( 1 σ ) > 1. Then there is a τ> and an n with m n<2m and s k τ −k s n τ −n for all k m. Hence, if s k > 0 for k m, τ k = O(s k ) and σ k = ... ⇐⇒ x, y < k and x  y or x, y k and ψ(x)  ψ(y) or x<k y and x  ψ(y). ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ ✏ r r r r r D z D ↑z I I ↑ Then D ↑z := (k+|I|,  ↑ ) is again a distributive latt...

Ngày tải lên: 07/08/2014, 06:23

... as: Włodarczyk and Plebaniak: Kannan-type contractions and fixed points in uniform spaces. Fixed Point Theory and Applications 2011 2011:90. Submit your manuscript to a journal and benefi t from: 7 ... now α 0 ∈ A and ε 0 > 0 be arbitrary and fixed, let n 0 =max{n 2 (a 0 , ε 0 ), n 3 (a 0 , ε 0 )} + 1 and let k, l Î N be arbitrary and fixed such that k>l>n 0 .Then,k...

Ngày tải lên: 20/06/2014, 21:20

... and strengthen Theorem 1.2 and the results due to Dotson [15], Jungck and Sessa [16], Lami Dozo [17] and Latif and Tweddle [18]. We also extend and unif y well-known results on fixed points and ... locally convex spaces and extends the corresponding results of Shahzad [20] to locally convex spaces. Theorem 3.3. Let T and f be selfmaps of a Hausdorff complete locally conv...

Ngày tải lên: 20/06/2014, 21:20

... and strengthen Theorem 1.2 and the results due to Dotson [15], Jungck and Sessa [16], Lami Dozo [17] and Latif and Tweddle [18]. We also extend and unif y well-known results on fixed points and ... p(x α − y)foranyy = x and p ∈ P. The Hilbert spaces and Banach spaces having a weakly continuous duality mapping satisfy Opial’s condition [17]. Al-Mezel Fixed Point Theory...

Ngày tải lên: 20/06/2014, 21:20