Báo cáo toán học: "On the number of permutations admitting an m-th root" pptx

... in the case when m is prime. Whether a permutation of n admits an m-th root can be read on the partition of n determined by the lengths of the permutation’s cycles, because the class of such the ... 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!foreachn....

Ngày tải lên: 07/08/2014, 06:23

... short proof of the factor theorem for finite graphs, Canadian Journal of Mathematics, 6 (1954), pp. 347–352. [38] W. T. Tutte, A census of planar triangulations, Canadian Journal of Mathematics, 14 ... 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 triangl...

Ngày tải lên: 07/08/2014, 21:20

... JOURNAL OF COMBINATORICS 5 (1998), #R20 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 ... can also be defined as the result of the insertion of the elements of a random permutation of {1, ,n}into an initially empty tree. Ascendants and d...

Ngày tải lên: 07/08/2014, 06:22

... on a cycle other than C 1 . Each has at least (d −4)n neighbours in C 1 and we can argue the existence of a 6-cycle as in the previous case. Remark: The proof shows that the number of Hamilton ... 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 graphs Alan Fri...

Ngày tải lên: 07/08/2014, 06:22

... f d cannot be the place of a notch, and the number of notches out of {f 1 ,f 2 , ,f d−1 } must be exactly by 1 larger than the number of notches out of {e 1 ,e 2 , ,e d−2 }. An example of a choice of notches ... 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...

Ngày tải lên: 07/08/2014, 08:22

... (5) the electronic journal of combinatorics 13 (2006), #N8 5 3 Start of the proof Let N = {0, 1, }. Define the weight of a matrix N to be the sum of its entries, and write |N| for the weight of ... of total degree at most n. This is true for the first term N((λ 1 , ,λ n−1 )) by the inductive hypothesis. Each of the subsequent terms is itself a sum. By the inducti...

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 ... multiple of the other by an element of the field. Let G P (q, d) denote the graph whose vertices are the points of P G(q, d) and two (not necessarily d...

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 ... e-graphs, and point E k+1 is the intersection of {E 1 , E 2 , . . . , E k+1 } and the points of the other of the e-graphs. Theorem 1. There can be at mo...

Ngày tải lên: 07/08/2014, 15:23

... −m)!. Multiply 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 deduce the lemma. ✷ Using the methods ... match as an edge. Then an m-matching of P k is composed of m edges and k −2m vertices. Altogether k −m objects. Hence the number of m-matchings...

Ngày tải lên: 07/08/2014, 21:20

... 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 of independent sets ... to the result in [1] that the Fibonacci numbers (of the paths) form a complete system of residues if and only if m = t · 5 k , t = 1, 2, 4, 6, 7, 14, 3 j where k  0, j  1 . 2 The...

Ngày tải lên: 08/08/2014, 11:20