Báo cáo toán học: "On the number of genus one labeled circle trees" doc

... such that the tree together with the circle it is drawn on can be embedded in a surface of genus one, but not of genus zero. Hough [3] observed that the number of genus one labeled circle trees ... offspring of C by definition. Proposition 4. The genus of the reduced form T 3 of a u-c-tree T is one if and only if the genus of T is one. Proof. L...

Ngày tải lên: 07/08/2014, 15:23

... 8 3. The number of descendants in random BSTs The number of the descendants D n,j of the j th node of a BST of size n is recursively computed as the number of descendants in the left subtree of the ... define the number of descendants D n,j as the size of the subtree rooted at the j th node, so we count the j th node as a descendant of itself...

Ngày tải lên: 07/08/2014, 06:22

... +2) ν n! ν!2 ν completing the proof of part (a) of Theorem 1. the electronic journal of combinatorics 7 (2000), #R57 5 Part 2 of the lemma follows from the chain of inequalities 1 φ(k) ≤ 1 γ(k 0 ) ≤ (β ... n)k −1 φ(k). In either case, the inequality in part 1 of the lemma holds. On the number of perfect matchings and Hamilton cycles in -regular non-bipartite gr...

Ngày tải lên: 07/08/2014, 06:22

... algebra, the radical of an ideal I is the set of all elements of the ring some positive power of which belongs to I; in the present situation, q(m)is the positive generator of the radical of the ideal ... is the exponential generating function (EGF, formal series) of the m-thpowersinthegroups n . This means that the number of m-thpowersin n is p n (m)×n!f...

Ngày tải lên: 07/08/2014, 06:23

... of the above theorem. Proof of Conjecture 1.2 for m ≥ 3d − e. The polynomiality in m of A X,Y (m)isobvious from (6.1) and Lemma 6.4. The assertion about the integrality of the coefficients of the “numerator” ... are not in one of these cases, then there is exactly one edge e attached to v which is below l.Theedgee is on a loop of the configuration. Let us start wi...

Ngày tải lên: 07/08/2014, 08:22

... conjecture of J. Benton, R. Snow, and N. Wallach in [1]. the electronic journal of combinatorics 13 (2006), #N8 2 Proof of Theorem 4. Wearefreetoassumen ≤ m. We define the function E of the variables ... polynomial in x and y of degree ≤ deg f +1. By induction and (4) it follows that the coefficients of G are rational numbers. This proves the lemma. 5 End of the proof S...

Ngày tải lên: 07/08/2014, 13:21

... q d 2 +k−1  q k−1 . From (2.6) and (2.8), the number of copies of K k in E is (1 + o(1)) |E| k k! q − ( k 2 ) . . This implies that the number of the number of k-tuples of k mutually orthogonal vectors ... J n q,d is the all one matrix and I n q,d is the identity matrix, both of size n q,d ×n q,d ). Therefore, the largest eigenvalue of V is D q,d and the a...

Ngày tải lên: 07/08/2014, 15:22

... each of these cases, the addition of two extra edges on one of the connecting tubes suffices to attain the genus bound in Lemma 3.1. Now in all twelve cases (for each of the twelve values of k) ... v α is one of the a i ’s or one of the b i ’s. Moreover, the edges on the tubes T i , i ≥ 1, may affect the connectivity of the graphs. So it is not easy to...

Ngày tải lên: 07/08/2014, 07:21

... condition for the boundedness of all solutions of (1.1) and the scalar case of (1.1), respectively. The next result provides a sufficient condition for the boundedness of solutions of (1.1). Theorem ... investigated, moreover the boundedness and estimation of the solutions are founded by using the resolvent of the equations. This article studies the boundedness...

Ngày tải lên: 20/06/2014, 20:20

Ngày tải lên: 05/08/2014, 10:20