Báo cáo toán học: "On certain integral Schreier graphs of the symmetric group" doc

... 1. the electronic journal of combinatorics 14 (2007), #R43 18 On certain integral Schreier graphs of the symmetric group Paul E. Gunnells ∗ Department of Mathematics and Statistics University of ... 2007 Mathematics Subject Classification: 05C25, 05C50 Abstract We compute the spectrum of the Schreier graph of the symmetric group S n corresponding to the Yo...

Ngày tải lên: 07/08/2014, 15:22

... terms of modular invariant theory of the general linear group at the prime p = 2. In [8], Hung and the author gave a mod-p analogue of the Singer invariant-theoretic description of the dual of the ... 2004 Dedicated to Professor Hu`ynh M`ui on the occasion of his sixtieth birthday Abstract The purpose of this paper is to give a mod-p analogue of the Lomonaco...

Ngày tải lên: 06/08/2014, 05:20

... calculation of the character of S n on the homology of the order complex of L A col , s n and using a formula of Orlik & Solomon [10] we are able to describe the character of S n on the cohomology of ... it appears in a generic fiber of a projection of the braid arrangement. The study of the intersection lattice of the arrangement leads to the defin...

Ngày tải lên: 07/08/2014, 06:20

... vertex of M, • −1 in turn to exactly one other vertex of M, • 0 to all other vertices of G. Then the constructed vectors constitute a simply structured basis of Eig(−1; G). Proof. According to Theorem ... the kernel of G has vanishing component sum, in particular the kernel basis vectors of G listed in Theorem 3.2. Hence, according to Theorem 3.4, together with the vector...

Ngày tải lên: 07/08/2014, 21:21

Ngày tải lên: 05/08/2014, 15:20

... Description of SMint The ”objects” of study in the continuous version of the multi-WZ theory are expres- sions of the kind  F (n, m, y, x)dx and identities between them. In the above general integral- sum, ... $100 for such a proof, provided it does not exceed the length of the present proof. Since a key to the integral evaluation is the package SMint,firstwegiv...

Ngày tải lên: 07/08/2014, 06:22

... the conditions in the statement of part (1). Let τ ∈ A n . Consider the circular class of τ consisting of the set {τ,τγ, ,τγ n−1 }. The proof of Lemma 2.1 shows that because τ(n)=n, we have the ... to be a descent of σ if σ(i) >σ(i +1). Definition 1.2 The major index of σ, denoted maj(σ), is the sum of the descents of σ. The values of the statistic ma...

Ngày tải lên: 07/08/2014, 06:23

... be the number of elements of S that are not vertices on any of the k + t edges of the matching. Then t + d + c of the edges are free. We are now prepared to construct the cycle containing the ... vertex). But neither ever exceeds t + d + c, the number of free edges. Hence, we may form a cycle containing the elements of S in the appropriate order. Proof of The...

Ngày tải lên: 07/08/2014, 07:21

... 2, with the following properties: the action of Aut(Γ i ) on the blocks of B is nonsolvable, doubly-transitive, but not a symmetric group, and the subgroup of Aut(Γ i )thatfixeseachblockofB set-wise is ... semiregular of order 2. If p =2 k − 1 > 7 is a Mersenne prime, these digraphs are also Cayley digraphs of the generalized quaternion group of order 2 k+1 .Inthis c...

Ngày tải lên: 07/08/2014, 07:21

... By Theorem 6, the expectation that a graph is a subgraph of a self-complementary graph H of the same order rises with the number of cycles of s-c permutation of H. 2 Main result We think that the ... evident that subgraphs of self-complementary graphs of the same order are embeddable. The relationship between the property “to be embeddable” and the property “to...

Ngày tải lên: 07/08/2014, 15:23