Báo cáo toán học: "The plethysm sλ[sµ] at hook and near-hook shapes" pot

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Ngày tải lên: 05/08/2014, 10:20

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Ngày tải lên: 05/08/2014, 10:20

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Ngày tải lên: 05/08/2014, 15:20

... g n is divisible by 5 if and only if (4 n − 1)  2n n  is divisible by 5. And since g n is odd, g n mod 10 = 5 if and only if g n is divisible by 5. 4 n −1 is divisible by 5 if and only if n is ... +( 1 4 ) 2  4 2  5 2 z 2 +···]. Hence, f n = 1 4 n  i= 0  2i i  2n − 2i n − i  5 i , and g n = 1 4 n  i= 0  2i i  2n − 2i n...

Ngày tải lên: 07/08/2014, 06:22

... Macdonald as a second special case. The main purpose of this paper is to give a planarized construction and proof for the bijection of Edelman and Greene between reduced words and certain pairs of ... Similarly a partial arrangement is an isomorphism class of simple marked partial arrangements of pseudolines. Goodman and Pollack [8] described a one-to-many corre...

Ngày tải lên: 07/08/2014, 06:22

... x]showsthats λ [s (1 a ,b) ][1 − x] = 0 unless λ is a hook. So we have shown that s [s à ]| hooks = 0 unless both and à are hooks, proving statement 1. If we now let λ =(1 c ,d), and for the ... is odd So statement 1 follows immediately by conjugating statement 1 of Theorem 4.5. When a is even, statement 6 follows by conjugating the formula in statement 6 of Theorem 4.5 and then subst...

Ngày tải lên: 07/08/2014, 08:20

... proof of this symmetry will induce a bijective proof of N(i, j)=N(j, i), and then a bijective proof of Lemma 6.4. Proof of Theorem 6.3. Let G(m, n)bethenumberofK-paths starting at (−2m, −2m) and ... negative, and the verification of the recurrence is straightforward. (We will give another proof of (48) in Example 9.2.) This completes the proof of (7). For equation (8), we n...

Ngày tải lên: 07/08/2014, 13:21

.. . ∆ 2 3,1 3 egAB x 2,3 , x 3,3 , ∆ 2 3,2 3 , ∆ 2 3,1 3 bdfA x 1,2 , x 2,2 , x 3,2 , ∆ 2 3,2 3 bfAC x 1,2 , x 3,2 , ∆ 2 3,2 3 , ∆ 1 3,2 3 fgAC x 3,2 , x 3,3 , ∆ 2 3,2 3 , ∆ 1 3,2 3 ceBF x 2,1 , x 2,3 , ∆ 2 3,1 3 , ∆ 1 2,1 3 acBF .. . x 1,1 , x 2,1 , ∆ 2 3,1...

Ngày tải lên: 07/08/2014, 15:23

... approach, the Weyl groups of type A n and C n are used to motivate a possible generalization to Weyl groups in general. For the construction of a basis for the Specht modules of Weyl groups, Halicioglu ... description of the Garnir relation associated with a ∆-tableau in terms of root systems. We then use these relations to find a K-basis for the Specht modules...

Ngày tải lên: 07/08/2014, 21:20

... all trees of diameter 4. Our main result is a proof of Conjecture 1 for all trees of diameter at most 5. Theorem 2. Let k, n ∈ N, and let G be a graph of order n so that at least n/2 vertices of ... subgraph of G. We prove the conjecture for all trees of diameter at most 5 and for a class of caterpillars. Our result implies a bound on the Ramsey n...

Ngày tải lên: 07/08/2014, 21:20

... p l } and we join vertices x and the electronic journal of combinatorics 15 (2008), #R126 10 The Ramsey number of diamond-matchings and loose cycles in hypergraphs Andr´as Gy´arf´as ∗ Computer and ... [12]) and t = 2 (Alon and Frankl [1] and Gy´arf´as [13]). Next we state and prove the Ramsey- type form of our main result, it determines the exact value of...

Ngày tải lên: 07/08/2014, 21:20

... Z´emor [36], on the other hand, proved the above result allowing |A| to be as large as po ssible, at the expense of requiring ǫ ′ to be small. 5 Proof of the main theorem (Theore m 1.6) By Theorem ... Hamidoune’s theorem and Karolyi’s theorem as corollaries, and thus, our main result provides purely combinatorial proofs for the Erd˝os-Heilbronn conjecture and an inverse Erd˝os-Hei...

Ngày tải lên: 08/08/2014, 01:20

... formed by adding terms with distinct indices, i. e.   i∈α x i : α ⊂ N, 0 < |α| < ∞  .) This is the content of the following theorem, the proof of which requires the following notion: ... combinatorial approach to the density Hales-Jewett theorem. Online project at http://michaelnielsen.org/polymath1/index.php?title=Polymath1; also D.H.J. Polymath, A new proof of the...

Ngày tải lên: 08/08/2014, 14:23

... is called the complete cd-index of [u, v], and it is denoted by  ψ u,v (c, d). Notice that the complete cd-index of [u, v] is an encoding of the distribution of the descent sets of each path ... including a characterization, of the complete cd-index of dihedral intervals. Furthermore, we describe a method to compute the complete cd-index of intervals in u...

Ngày tải lên: 08/08/2014, 14:23

... q)-analogs of the tangent and secant numbers, respectively. They may be rega rded as the graded forms of the traditional q -tangent and q -secant numbers T 2n+1 (q), E n (q) defined in (1.1) q and (1.2) q . ... := sin (r) q (u) cos (r) q (u) ;(1.8) sec (r) q (u) := 1 cos (r) q (u) ;(1.9) and define the (t, q)-analogs of the tangent and secant numbers as being the coeffic...

Ngày tải lên: 08/08/2014, 14:23