Báo cáo toán học: "Affine partitions and affine Grassmannians" docx

... ≥ 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 ... 1 4 )(itsdegreeis64), and [6, 3] and its irreducible restriction to A 9 is zero on elements of cycle types (2 4 , 1) and (3 2 , 1 3 ). Finally, the irreducible characters of A 10 (...

Ngày tải lên: 07/08/2014, 08:22

... of [A] and so α 1 = Υ 1 which gives Υ 1 = B 1 . On the other hand if we place 1s into every box of A we obtain a LR-tableau and so we have [n] ∈ [A] with n = |A| which gives us B 2 = 0 and so ... 1 and let A be a skew diagram which has one or more columns of length n. Rearranging the parts of A gives again a partition α whose corresponding character satisfies [α] ∈ [A] and α 1 = Υ 1...

Ngày tải lên: 07/08/2014, 15:22

Ngày tải lên: 05/08/2014, 15:20

... (423516) of w, and write w = w 1 ◦m◦w 2 , where ◦ denotes concatenation. Then form the tree T(w) by labeling the root with m and setting the left and the right subtrees of the root to be T (w 1 ) and T(w 2 ), ... =  n≥0 q ( n 2 ) x n /[n] q !, and d(σ) and inv(σ) denote the number of descents and inversions of σ, respectively. (Another good reference on the subject is a recent...

Ngày tải lên: 07/08/2014, 21:20

... article. Authors’ contributions OS and YS treated the patient and wrote the case report. HK and MTG critically revised the manuscript. All authors read and approved the final manuscript. ... imbalance between oxygen demand and supply, intense sympathetic stimulation, non-atherosclerotic coronary disease, coronary trauma, coronary vasospasm, coronary thrombosis, and endo...

Ngày tải lên: 20/06/2014, 20:20

... and MA carried out the design of the study and performed the analysis. MEO (adviser) participated in its design and coordination. All authors read and approved the final manuscript. References [1] ... = f(u, y) and f x : [c, d] → R, f x (v) = f(x, v) are convex where defined for all y ∈ [c, d] and x ∈ [a, b ]. Recall that SOME INTEGRAL INEQUALITIES 15 Computing the above integrals...

Ngày tải lên: 20/06/2014, 21:20

... vortex and adding lisozyme to a final concentration of 17 mg/mL. After incubation at 37 ºC for 1 h, proteinase K and SDS were added (final concentration of 0.7 mg/mL and 2 %, respectively) and ... students BMD, INSG and SPV carried out the DNA extraction and 16S rRNA gene libraries. EVSN provided the petroleum samples. EVSN, AJM and VMO are responsible for supervision and r...

Ngày tải lên: 20/06/2014, 21:20

... and R ⊂ B,andobviouslyR ⊃{a ∈ A : |a| >N+4c} and R ⊃ {b ∈ B : |b| >N+4c}.ThusA∆B is finite, and by Lemma 3 the result is established. Lemma 5 Let A, B ⊂  be locally finite infinite sets and ... m R+C (i) = m B 0 +C (i). Thus A 0 + C = B 0 + C and it follows from Lemma 2 that A 0 = B 0 and so A = B. Lemma 4 If A, B ⊂  are locally finite, infinite sets, and C is a finite set wit...

Ngày tải lên: 07/08/2014, 06:20

... reconstructed from the eigenvalues and main angles of its vertex deleted subgraphs. This follows from a formula connecting characteristic polynomials of a graph and its complement and main angles (see, for ... 99). References [1] D.M. Cvetkovi´c, M. Doob and H. Sachs, Spectra of Graphs - Theory and Applica- tions, Academic Press, New York 1980. [2] D. Cvetkovi´c and M. Lepovic, Se...

Ngày tải lên: 07/08/2014, 06:20

... (b 1 , ,b n )such that b 1 = 1and( b 2 , ,b n ) is a nondecreasing parking function. To see this, arrange the a i in increasing order, and consider m =max{a i −i | 1 ≤ i ≤ n} and j =max{i | a i −i = ... reflections. References [B1] P. Biane, Some properties of crossings and partitions. Discrete Math. 175 (1997), no. 1-3, 41–53. [B2] P. Biane, Minimal factorizations of a cycle and cent...

Ngày tải lên: 07/08/2014, 06:23