Báo cáo toán học: "On the number of orthogonal systems in vector spaces over finite fields" ppsx

... (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 in E is also (1 ... o(1)) |E| k k! q − ( k 2 ) , completing the proof of Theorem 1.2. Acknowledgments The research is performed during the author’s visit at the Erwin Schr¨odinger...

Ngày tải lên: 07/08/2014, 15:22

... 1 . 2 The number of matchings in a tree In t his section, we turn to the number of matchings in a graph. This is a lso known as the Hosoya index, or the Z-index in mathematical chemistry. For ... An interesting paper of Wagner [5] looks at the number of independent sets modulo m. Wagner showed that the pr oportion of trees on n vertices with the number...

Ngày tải lên: 08/08/2014, 11:20

... 1998. Abstract. The number of descendants of a node in a binary search tree (BST) is the size of the subtree having this node as a root; the number of ascendants is the number of nodes on the path connecting ... descendant of itself. The number of ascendants A n,j is the number of internal nodes in the path from the root of the tree to th...

Ngày tải lên: 07/08/2014, 06:22

... (d +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 ... segment containing x, the segment containing x  , and the remaining segment. Going round the cycle C i , starting at x  and ending at x, the vertices x, x ...

Ngày tải lên: 07/08/2014, 06:22

... is not the case. We approximate the c n (m) by the coefficients d n (m) of the expan- sion in power series of the principal part D m of C m in a neighbourhood of its dominant singularity 1. The sequences  d n−k (m)/d n (m)  n are ... is the exponential generating function (EGF, formal series) of the m-thpowersinthegroups n . This means that the number of m-...

Ngày tải lên: 07/08/2014, 06:23

... theorem (recalled in Lemma 2.3), to obtain a determinant for the number of rhombus tilings, see the proof of Lemma 6.4. In both cases, the polynomial nature of the number of rhombus tilings is immediately ... decomposes into the product of the number of possible configurations in the pentagonal region times the number of possible configurations in...

Ngày tải lên: 07/08/2014, 08:22

... notation, we have the following lemma. Lemma 6 Let a in N n+1 satisfy |a| = m. Then the number of x in N m such that a(x)=a is  m a  . Let λ =(λ 1 , ,λ n )=λ(x) be the column sums of the matrix R ... 6.2.5] or [3, Theorem 16.1], gives necessary and sufficient conditions for a pair of vectors to lie in RC m,n . Lemma 7 Let x in N m bethevectorofrowsumsofamatrixinM, and...

Ngày tải lên: 07/08/2014, 13:21

... point E 1 is the intersection of {E 1 , E 2 ,. . .,E k+1 } and the points of one of the e-graphs, and point E k+1 is the intersection of {E 1 , E 2 , . . . , E k+1 } and the points of the other ... even (since if 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...

Ngày tải lên: 07/08/2014, 15:23

... 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 the triangle is on the right of the ... 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-fa...

Ngày tải lên: 07/08/2014, 21:20

... :=  r i=1 A i . Let m ∈ min(p, q). Then perm m A is the number of m-matchings of G := ∨ r i=1 G i , which is equal to the number of m-matchings obtained in the following way. Consider m 1 , . ... all these choices to get the numerator of the right-hand side of (4.10). Divide this number of choices by the number of permutations of {1, . . . , rn} to ded...

Ngày tải lên: 07/08/2014, 21:20