Báo cáo toán học: "Ratio Monotonicity of Polynomials Derived from Nondecreasing Sequences" docx

... + 1) (m − k)(m + k + 1) < 1. the electronic journal of combinatorics 17 (2010), #N37 7 Ratio Monotonicity of Polynomials Derived from Nondecreasing Sequences Willia m Y. C. Chen 1 , Arthur ... relations of the coefficients. Keywords: log-concavity, ratio monotonicity, Boros-Moll polynomials. 1 Introduction This pap er is concerned with the ratio monotone prop erty of po...

Ngày tải lên: 08/08/2014, 11:20

... ratio monotonicity of the Boros-Moll polyno- mials, Math. Comp. 78 (2009), 2269–2282. [4] W. Y. C. Chen, A. L. B. Yang a nd E. L. F. Z hou, Ratio monotonicity of polynomials derived from nondecreasing ... f (n) k (x) of order n ≤ m − k has the same property. We establish this property by induction on n. the electronic journal of combinatorics 18 (2011), #P1 2 On the Modes...

Ngày tải lên: 08/08/2014, 12:23

... actually is a solution of the bibasic hypergeometric telescoping problem (1). This completes the proof of the correctness of Algorithm Telescope p,q . the electronic journal of combinatorics 3 (1996), ... of all coefficient-denominators of ¯ P,letg denote the greatest common divisor of all coefficients of l · ¯ P , and define z := g/l. Then, for P ∗ := z −1 · ¯ P , the bibasic moni...

Ngày tải lên: 07/08/2014, 06:20

... root of f 1 (x) = 0. This completes the proof. ✷ 3 The proof of The orems 1.5 and 1.6 We will need the following technical lemma whose proof is an easy modification of the proof of Theorem 2.2 from ... let e 12 be the size of G 12 . A theorem of Haemers [7] shows that eigenvalues of the quotient matrix of the partition interlace the eigenvalues of the adjacency matrix of...

Ngày tải lên: 08/08/2014, 12:23

... at 0. The the electronic journal of combinatorics 17 (2010), #R3 3 to be non-holonomic as soon as the set of of poles of φ(s) is not included in a finite union of arithmetic progressions with rational ... shape of the asymptotic expansion of a holonomic function at a singularity z 0 is strongly constrained, as it can only involve, in sectors of C, (finite) linear combinations of...

Ngày tải lên: 08/08/2014, 11:20

... V of a graph Γ = (V,E), the (local) proper polynomials constitute a sequence of orthogonal polynomials, constructed from the so-called u-local spectrum of Γ. These polynomials can be thought of ... distance” from each of their vertices. Afterwards, some new applications of both, the proper and adjacency polynomials, are derived, such as bounds for the radius of Γ and...

Ngày tải lên: 07/08/2014, 06:20

... lies on the boundary of Q and Γ triangulates the subcomplex of F(∂Q) consisting of all faces of Q which do not contain v. This is the complex of faces of Q which are not visible from a point beyond ... that ∆ is a triangulation of a polytopal complex F if the union of the faces of ∆ is equal to the union of the faces of F and every face of ∆ is contained in a face o...

Ngày tải lên: 07/08/2014, 08:22

... upper rank of the hypergraph – that is, the size of the largest hyperedge. The proofs of Theorems 1 and 2 involve the use of the combinatorial nullstellensatz [2]. the electronic journal of combinatorics ... #N22 2 A note on polynomials and f-factors of graphs Hamed Shirazi Jacques Verstra¨ete Dept of Combinatorics & Optimization Dept of Mathematics & Statistics Univ...

Ngày tải lên: 07/08/2014, 15:22

... Numbers of chromatic polynomials of degree at most 10. (A) Total number of chromatic polynomials, (B) number of chromatic polynomials of clique-separable g r aphs and (C) number of chromatic polynomials ... list the numbers of chromatic polynomials of degree at most 9 with certificates that use sequences of steps of the kind we have been discussing, with p ≥ 0. Exa...

Ngày tải lên: 07/08/2014, 21:21

... consequence of a refinement of a result of Carlitz, Scoville and Vaugha n [11] due to Stanley (cf. [33, Theorem 7.2]). Corollary 5.4. For all j = 0, . . . , n − 1, let W n,j be the set of all words of ... immediately from Theorem 1.2 and the definition of the M¨obius function. For a ranked poset P of leng t h n and r ∈ {0, 1 , . . . , n}, let W r (P ) be the rth Whitney number...

Ngày tải lên: 08/08/2014, 01:20