polynomials of maps and matrices

... skew-adjacency matrix of T → − the inverse of the skew-adjacency matrix of T and the negative of each eigenvalue of T is → − −1 → − −1 also an eigenvalue of T Therefore Sp( T ) = iSp(T −1 ) and hence E( ... and Gσ be an orientation of G The characteristic polynomials of G and Gσ are expressed as (2.1) and (2.4), respectively Because the roots of P (Gσ ; x) are pure imaginary and occur in complex conjugate ... the set of all linear subgraphs L of G with i vertices, p1 (L) is the number of components of size in L and p2 (L) is the number of cycles in L If G is bipartite, then = for all odd i, and the...

Ngày tải lên: 08/08/2014, 14:23

... Interesting Polynomials In this section, we define several polynomials involving combinatorial aspects of hypergraphs that are often studied Most of these polynomials generalize to well-known graph polynomials, ... polynomial of H in terms of coboundary polynomials of section hypergraphs of H This generalizes a result of Dohmen et al [DPT03] Proposition P (H; p, q, t) = S⊆V P (H × S; p, t)(q − p)|V |−|S| Proof ... paper of Dohmen et al [DPT03] By abuse of notation, we write e ⊆ π to mean the vertex set of e is a subset of some block of π Finally, let k1 (π) denote the number of singleton blocks of π Theorem...

Ngày tải lên: 08/08/2014, 14:23

... Control of e∂ ¯ 2.5.2 Analysis of neighbourhoods of antiholomorphic bubbles 2.5.3 Neck surgery and energy quantization 2.5.4 Assembly of the proof of Theorem 1.2 Heat flow — the proof of Theorem ... k ≥ and sufficiently large n Almost-harmonic maps — the proof of Theorem 1.2 The goal of this section is to understand the structure of maps whose tension field is small when measured in L2 , and ... sequence of maps satisfying the hypotheses of Theorem 1.2 Let us denote the set of antiholomorphic bubble points by A, and the holomorphic bubble points by H, and write Ξ for the set of all bubble maps...

Ngày tải lên: 28/03/2014, 22:20

... [0, ) and (3.14) implies (3.15), and the conclusion of Corollary 3.3 follows from Corollary 3.2 (b) Theorems 3.1-3.4 and Corollaries 3.1 and 3.2 all generalize and improve [5, Theorem 3.4] and ... of all nonempty subsets of X, C (X) the family of all nonempty closed subsets of X and CB (X) the class of all nonempty closed bounded subsets of X, respectively For any A, B ∈ CB (X) , define ... metric space and p: X × X ® [0, ∞) a τ-function For each x Î X and A ⊆ X, let d(x, A) = inf d(x, y), y∈A and p(x, A) = inf p(x, y) y∈A Denote by N (X) the family of all nonempty subsets of X, C (X)...

Ngày tải lên: 20/06/2014, 22:20

... purpose of this paper is to present a systemic study of some families of higher-order generalized q-Genocchi numbers and polynomials attached to χ by using the generating function of those numbers and ... Govil and Gupta 10 have introduced a new type of q-integrated Meyer-Konig-Zeller-Durrmeyer operators, and their results are ¨ closely related to the study of q-Bernstein polynomials and q-Genocchi ... function of those numbers and polynomials Generalized q-Genocchi Numbers and Polynomials For r ∈ N, let us consider the q-extension of the generalized Genocchi polynomials of order r attached to χ...

Ngày tải lên: 21/06/2014, 05:20

... systemic study of some formulas of the twisted q-extension of the generalized Euler numbers and polynomials of order k attached to χ On the Twisted q-Extension of the Generalized Euler Polynomials ... q-analogue of the p-adic log gamma functions and related integrals,” Journal of Number Theory, vol 76, no 2, pp 320–329, 1999 T Kim, “Some identities on the q-Euler polynomials of higher order and q-Stirling ... of Mathematical Physics, vol 10, no 3, pp 261–267, 2003 13 S.-H Rim, S J Lee, E J Moon, and J H Jin, “On the q-Genocchi numbers and polynomials associated with q-zeta function,” Proceedings of...

Ngày tải lên: 21/06/2014, 16:20

... pp 44–56, 2007 L Jang and T Kim H Ozden, I N Cangul, and Y Simsek, “Remarks on sum of products of h, q -twisted Euler polynomials and numbers,” Journal of Inequalities and Applications, vol 2008, ... purpose of this paper is to give the distribution of extended higher order q-Euler and q-Genocchi polynomials In 24 , Choi-Anderson-Srivastava have studied the q-extension of the Apostol-Euler polynomials ... 987– 1000, 1948 Y Simsek, V Kurt, and D Kim, “New approach to the complete sum of products of the twisted h, q -Bernoulli numbers and polynomials, ” Journal of Nonlinear Mathematical Physics,...

Ngày tải lên: 22/06/2014, 03:20

... 45–49, 2001 14 H Ozden, Y Simsek, and I N Cangul, “Remarks on sum of products of h,q -twisted Euler polynomials and numbers,” to appear in Journal of Inequalities and Applications 15 Y Simsek, “Theorems ... polynomials and numbers, see 14, 15 In this paper, we consider the new q-extension of Euler numbers and polynomials to be different which is treated by Ozden et al From our q-Euler numbers and polynomials, ... Journal of Inequalities and Applications Higher-order q-Euler numbers and polynomials In this section we also assume that q ∈ Cp with |1 − q|p < Now we study on higher-order q-Euler numbers and polynomials...

Ngày tải lên: 22/06/2014, 06:20

... orbit of x under f O(x) is usually regarded as a set of points, while sometimes it is regarded as a sequence of points Denote by Z+ the set of all nonnegative integers, and denote by N the set of ... {ρ(x) : x ∈ X } = (2.5) Fixed Point Theory and Applications The proof of Theorem 2.3 is similar to that of Theorem 2.2, and is omitted In [16], Sharma and Thakur discussed the condition d f (x), ... of f on O(v, f ) is bounded Proof It follows from (3.17) and Theorem 3.9 that the moving distance of f m on O(v, f ) is bounded Therefore, by (3.17) and the proof of Theorem 3.4, v, f m (v), f...

Ngày tải lên: 22/06/2014, 19:20

... hemicontinuity of setvalued maps in E and prove various new results concerning the existence of zeros of Φ, coincidences of F and G and fixed points of F in which transfer positive hemicontinuity and strictly ... ) and the maps Fi and Gi satisfy the assumptions of Theorems 2.9(iii) and 2.9(iv), respectively, i = − The pair (Fi ,Gi ) and the maps Fi and Gi satisfy the assumptions of Theorems 2.10(iii) and ... (C), F3 (c) and G3 (c), c ∈ C, are compact and convex and F3 and G3 are s.t.p.h.c and t.p.h.c on C (thus also s.t.h.c and t.h.c by Proposition 2.4, Remark 2.2 and Definitions 2.1 and 2.3) but...

Ngày tải lên: 23/06/2014, 00:20

... right If S is monotone, Brualdi and Sanderson [2] defined the discrepancy d(A) ¯ of A to be the number of positions in which A has a and A has a It equals the ¯ number of 1’s in A which have to be ... S1 T1 and S2 T2 since l si = l ti Also S1 and S2 are monotone since i=1 i=1 S = (S1 , S2 ) is Now we consider the partition of A = [A1 A2 ], where A1 and A2 are m × l and m × (n − l) matrices, ... 2, and The intersection of each row of A with region i is connected for each i = 1, 2, and define, for each A ∈ A(R, S), the discrepancy d(A) of A to be the number of 1’s of A in region 2, then...

Ngày tải lên: 07/08/2014, 06:20

... sequence and PG2 (x) = PH2 (x), PG3 (x) = PH3 (x) Moreover, the characteristic polynomials of the pairs G7 , H7 , G11 , H12 and G12 , H11 differ only in their respective coefficients of x The list of ... -1 -1 0 0 0 0 0 0 Table 1: Coefficients of the characteristic polynomials of the graphs of Figure and their vertex-deleted subgraphs 7 the electronic journal of combinatorics (2000), #R12 G • HH ... reconstructed from the eigenvalues and main angles of its vertex deleted subgraphs This follows from a formula connecting characteristic polynomials of a graph and its complement and main angles (see, for...

Ngày tải lên: 07/08/2014, 06:20

... properties of nonnegative matrices and their permanents, Soviet e Math Dokl 14:945-949 (1973) [4] R A Brualdi, J L Goldwasser and T S Michael, Maximum permanents of matrices of zeroes and ones, ... greatest root of ρ(R, x) Theorem Suppose S = Sm,k and R ∈ L(k, mk) Let λS and λR be the largest roots of ρ(S, x) and ρ(R, x) respectively Then λR ≥ λS and wr (R) ≥ wr (S) for all r Proof: Let v be ... w) Proof: We prove only (a) and (b); the proofs of (c) and (d) being similar Let {λi }n i=1 be the roots of ρ(R, x), labelled in non-decreasing order Suppose x is in the interval (k, λn ) and choose...

Ngày tải lên: 07/08/2014, 06:22

... conjecture of J Benton, R Snow, and N Wallach in [1] the electronic journal of combinatorics 13 (2006), #N8 Start of the proof Let N = {0, 1, } Define the weight of a matrix N to be the sum of its ... polynomial in x and y of degree ≤ deg f + By induction and (4) it follows that the coefficients of G are rational numbers This proves the lemma End of the proof Since G is a polynomial of degree ≤ ... be the vector of row sums of a matrix in M, and set λ = λ(x) Then (x, y) ∈ RC if and only if y ∈ Nn satisfies (i) |y| = |λ|, and (ii) yσ λ for all σ ∈ Sn the electronic journal of combinatorics...

Ngày tải lên: 07/08/2014, 13:21

... permutations and pairs of standard Young tableaux, and its generalisation by Knuth to matrices and semistandard Young tableaux (the RSK correspondence) are intriguing not only because of their many ... independently of this argument that the right hand sides of (7) and (8) describe the same values as those of (3) and (6) Although for the two factors of the summand of (1) or (4) we can thus apply cancellations ... instead of an insertion process, and that in this approach the use of Greene’s invariant and elementary Knuth operations can be avoided A drawback of this point of view is that the complications of...

Ngày tải lên: 07/08/2014, 13:21

... the set of tree-rooted maps the electronic journal of combinatorics 14 (2007), #R9 of size n and the Cartesian product of the set of trees of size n and the set of non-crossing partitions of size ... tree-rooted maps of size n and pairs consisting of a tree and a non-crossing partition of size n and n+1 respectively This simple bijection explains why the number of tree-rooted maps of size n ... bijection between tree-oriented maps (of size n) and pairs made of a tree and a non-crossing partition (of size n and n + respectively) 3.1 Tree-rooted maps and tree-oriented maps In this subsection,...

Ngày tải lên: 07/08/2014, 15:22

... Truncations of random unitary matrices have been the subject of several recent articles (see [3], [5], [8]) Interest in truncations of random unitary matrices stems from their relation to the physics of ... likely analogues of Theorem for truncations of random orthogonal and symplectic matrices Acknowledgements I am grateful to Roland Speicher and Jamie Mingo for helpful discussions, and to Richard ... partitions λ of n and f λ denotes the number of Standard Young Tableaux of shape λ The significance of this result is that, by the RSK correspondence, λ λ n, (λ)≤d (f ) is the number f (n, d) of permutations...

Ngày tải lên: 07/08/2014, 15:22

... main theorem of the paper: the equality of doubly refined enumerations of Alternating Sign Matrices and of Totally Symmetric Self-Complementary Plane Partitions Section contains the proof, based ... all permutations of the axes of the cube of size 2n×2n×2n; and taking the complement, that is putting cubes where they are absent and vice versa, and flipping the resulting set of cubes to form ... connect ASMs and TSSCPPs Building on the already mentioned ASM conjecture by Mills and Robbins, which says that the number of ASMs of size n is equal to the number of TSSCPPs of size 2n (and which...

Ngày tải lên: 07/08/2014, 21:20

... simulataneously interchanging rows and and columns and of the matrices I, M3 and M3 Thus, by simulataneous interchanging points and and blocks and of every parallel class of points and blocks, the inverse ... numbers A4 and A6 of codewords of weights and 6, and the order # Aut of the automorphism group of Ci By [15, Theorem 13], the weight enumerator of a Hermitian self-dual code of length 18 and minimum ... of C and the set of all automorphisms of C forms the the electronic journal of combinatorics 17 (2010), #R171 automorphism group Aut(C) of C The number of distinct Hermitian self-dual codes of...

Ngày tải lên: 08/08/2014, 12:23

... components of the point (x, y) ∈ , x and y, are both algebraic, each will be algebraic of degree no more than if we can find matrices B and A, where both B and A can be written as products of matrices ... form of all 216 TRIP maps and the corresponding inverses We proceed to construct recurrence relations for certain classes of these maps; afterward, we present two ways of visualizing the action of ... Tσ,τ0 ,τ1 Combo TRIP Maps and Polynomial-Growth We obtain a larger class of maps by allowing compositions of TRIP maps [2] As an example, we might perform the first division of using the permutation...

Ngày tải lên: 21/09/2015, 21:26