Báo cáo toán học: "Combinatorial Identities from the Spectral Theory of Quantum Graph" potx

... 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 ... orthogonal polynomials of integers x with 0 ≤ x ≤ N.Theyhave quite diverse applications ranging from the theory of covering codes [6] to the statistical mechanics...

Ngày tải lên: 07/08/2014, 06:23

Ngày tải lên: 05/08/2014, 15:21

... 5, µ 2 ∆ ≥  n t  4 p 2t 2 t 2  n t  2 p 2t 2 ϕ(1, 1) 10 the electronic journal of combinatorics 4 (1997), #R18 6 2. PROOFS Proof of the Theorem: We have already provided a proof of the second part of the theorem using nothing more ... decrease. The proof of the theorem proceeds by a sequence of lemmas: Lemma 1. The function ψ(r, c), extended to the closed domai...

Ngày tải lên: 07/08/2014, 06:20

... 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

... explicitly,  2n n  = n  k=0  n 2k  2k k  2 n−2k . (37) Proof: The total number of elements of NC B n is obtained as the sum of the cardinalities of the boolean lattices in the SBD of Theorem 3. There are  n 2k  2k k  choices ... the statistics suv(b): = the sum of the values which are not barred in b, sup(b): = the sum of the positions of the s...

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 ... (10 −8 ) the electronic journal of combinatorics 7 (2000), #R39 9 We have thus obtained Theorem 2 part (b). The error term therein follows from (3.3). We proceed to analy...

Ngày tải lên: 07/08/2014, 06:20

... 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...

Ngày tải lên: 07/08/2014, 07:21

... matroid (Theorem 8. 9of[ 3]). The proof of Theorem 1.3 is based on the following lemmas regarding the half–plane property. The paper [3] gives a much more thorough development of the theory. the electronic ... that the sum of the weights of the edges of G is at least (k +1)Ψ k+1 MS, completing the proof.  Unfortunately, it is not hard to find planar graphs which...

Ngày tải lên: 07/08/2014, 08:22

... s  ,thepowerofy does not change in the passage from D  to D.Thepowerofw does not change either, since there are the same number of extra cells left of the last vertical move after adding the ... i,let(a, c) be the coordinates of the southeast corner of S i ,andlet(b, c) be the coordinates of the southwest corner of S i . First note that c = v 0 + v 1 + ···+ v i...

Ngày tải lên: 07/08/2014, 08:22

... which of these two is genuine and which is the impostor. (In the setting of G-words, the condition 1 ∈ b tells us which is which.) Theorem 2 follows immediately from Lemmas 3–6, which describe the ... 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...

Ngày tải lên: 07/08/2014, 21:21