Báo cáo toán học: "A Multivariate Lagrange Inversion Formula for Asymptotic" pps

... a i,j . A traditional formulation of multivariate Lagrange inversion is Theorem 1. Suppose that g(x),f 1 (x),···,f d (x)are formal power series in x such that f i (0) = 0for 1 ≤ i ≤ d. Then the ... combinatorial proof of the multivariate Lagrange inversion formula, J. Combin. Theory Ser. A 45 (1987) 178–195. [5] I. P. Goulden and D. M. Kulkarni, Multivariable Lagrange invers,...

Ngày tải lên: 07/08/2014, 06:22

... atomic formulas of the form x ∈ X expressing the membership of x in a set X. In order to write more readable formulas, we will also use their negations x /∈ X. The syntax also allows atomic formulas ... combinatorics 15 (2008), #R69 23 5.3 Multivariate polynomials defined by MS formulas and sub- stitutions For an MS formula ϕ with free variables among X 1 , . . . , X m , for a graph G,...

Ngày tải lên: 07/08/2014, 21:20

Ngày tải lên: 05/08/2014, 15:20

... reciprocity law. A complicated formula for this law has been known for about fifty years, but recently Gessel and the present author independently obtained a much more elegant formula, as a corollary ... Here, fol- lowing a suggestion of Goldman, we provide a direct combinatorial proof of this new formula. MR primary subject number: 05A19 MR secondary subject numbers: 05A05, 05A15 A b...

Ngày tải lên: 07/08/2014, 06:20

... y k for some k with k<n. Now we consider two cases. If y k+1 is not a vertex of X,then we replace the edge x n−1 x n with the edge y k+1 x 0 to create a third path of length n.If y k+1 = x i for ... distinct from X and Y . Proof. Label the vertices of X as x 0 ,x 1 , ,x n ,withx i−1 adjacent to x i for 1 ≤ i ≤ n. Similarly, label the vertices of Y as y 0 ,y 1 , ,y n .Lets be the numb...

Ngày tải lên: 07/08/2014, 06:23

... See [1] for background on the chromatic polynomial. We define an increasing G-connected forest R to be a forest where each component R| s(R) i is an increasing G| s(R) i -connected tree. For a graph ... a G-connected tree need not be a subgraph of G and that G must be connected for any rooted tree to be G-connected. Definition 2 For each connected graph G on a totally ordered vertex set...

Ngày tải lên: 07/08/2014, 08:22

... sufficient to prove that the formula holds for f(t)=e tx : If the formula is true for f(t)=e tx , then comparing coefficients of x n /n!on both sides we get that the formula holds for f (t)=t n . But this ... holds for f (t)=t n . But this implies by linearity that the formula is true for all admissible formal power series f. To prove the formula for f(t)=e tx ,wehave e Mz e...

Ngày tải lên: 07/08/2014, 13:21

... for any σ ∈ S 2k . We call a permutation cycle χ minimal if it is a transposition or if µ ι = ν ι = 2 for all ι. Minimality implies that we can write our general permutation cycles χ in the form χ ... Conjecture for 3-pillows, pre- sented in Section 5.3. Through experimental calculations, I have expanded and extended the conjecture. For one, I extend the conjecture to odd pillows. Fo...

Ngày tải lên: 07/08/2014, 13:21

... function for L P can be written as a rational function: Ehr P (t) :=  m≥0 L P (m)t m = δ 0 + δ 1 t + . . . + δ k(n+1)−1 t k(n+1)−1 (1 − t k ) n+1 , whose coefficients δ i are non-negative. For an ... for all v ∈ P }. If the origin lies in the interior of P then P ∨ is a rational polytope containing the origin, and P = (P ∨ ) ∨ . We restrict our attention to those P containing the origin...

Ngày tải lên: 07/08/2014, 15:22

... induction hypothesis d(a, x) ≤ k − 1, which is a contradiction. Therefore (k − 2)r 2 + 1 ≤ |Supp(x) ∩ Supp(a)| ≤ kr 2 , which is the form required for x. Conversely, given x which satisfies these inequalities then ... ∩ X) \ {a}. Now consider x ∈ ∆ 2 (a). Then x ∈ ∆ 1 (y) for some y ∈ ∆ 1 (a). Now x /∈ y and y /∈ a, for otherwise x ∈ ∆ 1 (a). Therefore Supp(x) ∩ Supp(y) = ∅ and Supp(...

Ngày tải lên: 07/08/2014, 21:21