Báo cáo toán học: "Linear Recurrence Relations for Sums of Products of Two Terms" ppt

... electronic journal of combinatorics 18 (2011), #P170 13 Linear Recurrence Relations for Sums of Products of Two Terms Yan-Ping Mu ∗ College of Science, Tianjin University of Technology Tianjin ... 05A19 Abstract For a sum of the form  k F (n, k)G(n, k), we set up two systems of equations involving shifts of F (n, k) and G(n, k). Then we solve the systems by ut...

Ngày tải lên: 08/08/2014, 14:23

... number of σ in the symmetric group S n of degree n. We give an algebraic proof and a combinatorial proof of the recurrence relation. 1 Introduction Let S n denote the symmetric group of degree ... A recurrence relation for the “inv” analogue of q-Eulerian polynomials Chak-On Chow Department of Mathematics and Information Technology, Hong Kong Institute of Education, 10 Lo...

Ngày tải lên: 08/08/2014, 11:20

... element of wJ ∩ Ψ − can be of the form −2e i for some i, and so −2e i ∈ wJ (2) . Now, put −α ∗ = 2e i . Then by definition of the set J −α ∗ , all the elements of wJ  occur in J −α ∗ except for the ... combination of the polytabloids the electronic journal of combinatorics 15 (2008), #R73 13 The main object of this paper is to construct the Garnir relations in terms of t...

Ngày tải lên: 07/08/2014, 21:20

... point of T, {ε n } is a sequence of positive numbers for which lim n→∞ ε n = 0, and {y n } ⊆ X w satisfies w λ (y n+1 , T y n ) ≤ ε n for all λ > 0. Then, lim n→∞ y n = x 0 . Proof. For each ... Tu, so T u is a fixed point of T N . By the uniqueness of fixed point of T N , we have Tu = u. Thus, u is a fixed point of T . Since fixed point of T is also fixed point of T N , we...

Ngày tải lên: 20/06/2014, 21:20

... proof.  Proposition 3.2. (1) γ(n, n − 1) = γ r (n, n − 1)= 1for any n ≥ 1. (2) γ(n, n − 2) = γ r (n, n − 2)= 1for odd n ≥ 2. (3) γ(n, n − 2) = γ r (n, n − 2)= 2for even n ≥ 2. Proof. For each of ... three of the two element A v ’s that contain z and at least three, that contain w. So it is clear that we cannot avoid having either two A v ’s of the form {x, z} and {y,w} or, of...

Ngày tải lên: 07/08/2014, 06:20

... entry in the table of values of γ(n, δ)in[2] Acknowledgement We wish to thank Gordon Royle for providing Cayley tables for the 14 groups of order 16 and Cayley graphs of groups of orders up to 31. References [1] ... }. the electronic journal of combinatorics 7 (2000), #R58 17 5 Exact values of δ 3 (n) for small n. In this section we give exact values of δ 3 (n) for 6 ≤...

Ngày tải lên: 07/08/2014, 06:22

... combinatorial properties of these statistics, obtaining an explicit summation formula for their generating function and giving bijective proofs of the equivalence of different pairs of statistics. As before, these ... ) t x 0 (f) n  j=1 count(f,j). (21) Proof. In light of formula (20) and its proof, we need only show that h 1 (P )+h 2 (P )=x 0 (f) for all P ∈P n,k,m (f). Recall...

Ngày tải lên: 07/08/2014, 08:20

... that every vertex of N ∪ P is adjacent to a vertex of D  . Of course, some of the sets could also be empty for some dominating sets. If A and B are two subsets of the vertex set of a graph we say ... denote the set of vertices of V (G) \ D G which are adjacent to a vertex of D  G but are not private neighbors of any vertex of D  G .Set D  G = D G \ D  G denotin...

Ngày tải lên: 07/08/2014, 08:22

... a formula due to G. Labelle for the summed cycle indices of all rooted trees, which resembles the well-known formula for the cycle index of the symmetric group in some way. An elementary proof ... method is widely used for graph enumeration problems – we refer to [6] and the references therein for instance. For the application of this method, information on the cycle indices...

Ngày tải lên: 07/08/2014, 13:21

... As the set of spokes form an edge-cut of the graph W (n, 2k +3), such a cycle must in fact use an even number of spokes. If the number of spokes used is four or more then the number of vertices ... no cycle of length l exists. Lemma 4 For any edge e in the complement of W (n, 2k +3) and k ≥ 7, the graph W (n, 2k +3)+e contains a cycle of length l =2k +3. Proof: We divide the...

Ngày tải lên: 07/08/2014, 13:21