Báo cáo toán học: "The Abel-type polynomial identities" pps

... characteristic polynomial of G is the characteristic polynomial of its adjacency matrix A and is defined by P G (x)=det(xI − A). We call the collection of the char- acteristic polynomials of the ... 2000. Abstract The question of whether the characteristic polynomial of a simple graph is uniquely determined by the characteristic polynomials of its vertex-deleted sub- graphs is one of the...

Ngày tải lên: 07/08/2014, 06:20

... results, we introduce the cube polynomial of agraphG as c(G, x)=  i≥0 α i (G)x i . (For other graph polynomials see [6].) We first show some basic properties of the cube polynomial: the amalgamation, ... Then the cube polynomial c(G, x)ofG is introduced as  i≥0 α i (G)x i . It is shown that any function f with two related, natural properties, is up to the factor f(Q 0 ,x) the cube poly...

Ngày tải lên: 07/08/2014, 07:21

... m + 3 and n + m + 4. Suppose the electronic journal of combinatorics 17 (2010), #R10 4 The Abel-type polynomial identities ∗ Fengying Huang School of Mathematical Sciences, South China Normal ... iz) n−i , where x, y and z are real numbers. In this paper we deduce several polynomials expansions, referred to as Abel-type identities, by using Foata’s method, and also show some of their ap...

Ngày tải lên: 08/08/2014, 11:20

... numbers of any P -polynomial scheme (cf. [5, p. 199]). In their book on association schemes, Bannai and Ito made the dual conjecture. 1.2 Conjecture. [1, p. 205] If Y is Q -polynomial with respect ... The Terwilliger algebra for bipartite P -andQ -polynomial asso- ciation schemes, in preparation. [4] J. S. Caughman IV, Spectra of bipartite P -andQ -polynomial association schemes, Graphs C...

Ngày tải lên: 07/08/2014, 06:22

... λ. It is not hard to see that Res(f(z),z = λ) may be expressed in the form u λ (t)λ −t for some polynomial u λ (t), and thus it follows from our earlier discussion that − Res(f(z),z = λ)=P A,λ −1 (t)λ −t .In particular, P A (t)=− ... Brooks/Cole, Mon- terey, California, 1986. the electronic journal of combinatorics 8 (2001), #N7 5 The polynomial part of a restricted partition function rel...

Ngày tải lên: 07/08/2014, 06:22

Ngày tải lên: 07/08/2014, 07:21

... A). The 2-variable graph polynomial T (G; x, y), known as the Tutte polynomial of G, is defined as T (G; x, y) =  A⊆E (x − 1) r(E)−r(A) (y − 1) |A|−r(A) . (1) The Tutte polynomial of G has many ... Merino, C.: Chip-firing and the Tutte polynomial. Annals of Combinatorics, 1, 253– 259, 1997. [9] Plautz J. and Calderer, R.: G-parking functions and the Tutte polynomial. Preprint. [10] Sta...

Ngày tải lên: 07/08/2014, 15:22

... with coefficients in Q(q) as a q-parameter family of polynomials in two commuting variables. More precisely, th e coefficients of the annihilating polynomial P f given by (28) define a function F : ... (30) is achieved at least twice. Although (30) may have non quasi -polynomial solutions, Th eorem 1.1 suggests to look for quadratic quasi -polynomial solutions of (30). It turns out that those...

Ngày tải lên: 08/08/2014, 14:23

Ngày tải lên: 20/06/2014, 20:20

Ngày tải lên: 20/06/2014, 20:20