Báo cáo toán học: "Restricting supercharacters of the finite group of unipotent" docx

... Further, in the case in which the out-degree of each vertex of G is a fixed integer k, we show the kernel of this surjection is the k-torsion subgroup of K(LG, e ∗ ). These results appear as Theorem ... exposition of the properties of the sandpile group, the reader is referred to [2]. In his paper, [3], Levine shows that if e ∗ = (w ∗ , v ∗ ), then κ(G, w ∗ ) divides...

Ngày tải lên: 08/08/2014, 14:23

... = S λ , then a vertex of S sees u 1k or u jk if and only if either u jk is not South of the end of a tine but on a tine of S, or u jk is South of the end of a tine and weakly North of the next ... subgroups of the finite general linear groups GL n (F q ); the group U n is the pattern group corresponding to the total order 1 < 2 < 3 < · · · < n....

Ngày tải lên: 07/08/2014, 21:21

Ngày tải lên: 05/08/2014, 15:21

... D(n). Proof. Consider the table of the characters χ N ; we are interested in the dimension of the row-span of this table. Since the dimension of the row-span of a matrix is equal to the dimension of ... well study the dimension of the space spanned by the columns of the table. By the preceeding lemma, the N th entry of the column corresponding to...

Ngày tải lên: 07/08/2014, 06:20

... bounded, then the height distribution concentrates on two consecutive points. 3 Derivation of Results We establish the five parts of Theorem 2. Since the analysis involves a routine use of the saddle ... in the same way except that at the k-th step, the splitting of sets is based on the k-th symbol of the underlying strings. ∗ This work was supported by DOE Grant DE...

Ngày tải lên: 07/08/2014, 06:20

... proof of Theorem 2. 2.2 Proof of Theorem 3 Here we assume that s 2 ≥  2 n,thecases 1 ≥  2 nis similar. Denote by P r the product of the primes not exceeding r. The rough outline of the proof will ... G(A)forl> n 6 . In the proof we will distinguish two cases depending on the size of |A (6,1) | + |A (6,5) | .The theorem will be an immediate consequence of the fo...

Ngày tải lên: 07/08/2014, 06:22

... orbits. In the present case a family is completely specified by the integer q ≡ q 1 which counts the traversals of the loop 1, i.e., the number of letters 1 in the code word. Each of these q letters ... operator u n =trU n (19) as sums of periodic orbits of the graph. The two-point correlations in the spectrum of S (16) can be expressed in terms of the average...

Ngày tải lên: 07/08/2014, 06:23

... subset of vertices (or edges). The subgraph obtained from G by deleting the vertices in V  together with their incident edges is denoted by G − V  . The graph obtained from G by adding a set of ... v)andd(u, X). The length of a shortest cycle in a graph G is called the girth of G. Clearly, adding edgestoagraphG might decrease the girth of G.IfG  is obtained from G by...

Ngày tải lên: 07/08/2014, 07:21

... fixing 1, . . . , r. Then the map φ : Γ(A n (1, . . . , r)) → the electronic journal of combinatorics 14 (2007), #R25 4 Proof of Theorem 2.1. We shall imitate the proof of Theorem 4.2 in [8] by ... contradicting the maximality of I. So |I| = (m − 1)!m(n − 1)!. Again, the maximality of I implies that m = n and so I has the required shape as above.  Proof of Theorem 1.4...

Ngày tải lên: 07/08/2014, 15:22

... x i ) ∈ C be the slope of ℓ ij . Let A = C[m ij ], and let I n ⊂ A be the ideal of algebraic relations on the slopes m ij that hold for all choices of the points p i . Order the variables of A lexicographically ... upd own (or Euler) numbers, thereby obtaining a formula for the number of generators of the initial ideal of I n in each degree. The symbol N will den...

Ngày tải lên: 07/08/2014, 21:21