Báo cáo toán học: "n the number of distributive lattices" ppsx

... inequalities are the numbers v k of vertically indecomposable distributive lattices of size k. We present the explicit values of the numbers d k and v k for k<50 and prove the following exponential bounds: 1.67 k <v k < ... lattices, one rather considers the vertical sum in that case, where the only difference to the former is that now the top element  1 of...

Ngày tải lên: 07/08/2014, 06:23

... 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 ... where q is the quadratfrei radical of m. The order of the singularity 1 is clearly  µ(k)/k, where the sum extends to all divisors of q. Let ϕ be the...

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” ... between the rhombus tilings in the statement of the theorem and these semistandard tableaux. Proof of Theorem 2.2. It should be observed that, due to th...

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

... observation that the number of edges in Γ π,0 equals the number of permutations σ that are covered by π in the strong Bruhat 1 order on S n , and the number of edges in G π,0 equals the degree of the vertex ... are in the case of the second diagram). Since l and t are adjacent, the number of diagram points that lie in region A of the diagram is bounde...

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 abs...

Ngày tải lên: 07/08/2014, 15:22

... K 1 and K 2 are identical, then the number of edges in K 1 and K 2 is the same, thus the sum of the number of edges in K 1 and K 2 is even, and on the other hand it is n−2 2 ). Therefore, in case n−2 2 is ... T 2 is a subgraph of the tree T 3 , the set of vertices of T 2 is equal to the set of vertices of T 3 , and there are exactly n p − n e − 1 edges of...

Ngày tải lên: 07/08/2014, 15:23

... either none or both of the edges. Let c G be the number of 2-factors of G. Among the 2-factors of G  (k) let S denote the set of those, which induce a 2-factor of G, and S c the other 2-factors. ... from the source to the sink of ∆. We say that ∆ is a + triangle of B if looking along the direct source-sink edge the triangle is on the left. Otherwise, if...

Ngày tải lên: 07/08/2014, 21:20