Báo cáo toán học: " DIAGONAL CHECKER-JUMPING AND EULERIAN NUMBERS FOR COLOR-SIGNED PERMUTATIONS" pps

... ∈ [n], we include arcs between i and j and between −i and −j if π contains e i −e j , an arc between i and −j if π contains e i + e j and arcs between i and 0 and between the electronic journal ... partitions. From now and on we choose Φ and Φ + explicitly as in [10, 2.10], so that positive roots are of the form e i ,2e i and e i ± e j for i<j, where the e i denote st...

Ngày tải lên: 07/08/2014, 06:22

... ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for nonassociative products, Bull. Amer. Math. Soc., 54 (1948), 352–360. [21] R. Simion and W. ... Donaghey and L.W. Shapiro, Motzkin numbers, J. Combin. Theory Ser. A, 23 (1977), 291–301. [12] E. S. Egge and T. Mansour, Permutations which avoid 1243 and 2143, continued fractio...

Ngày tải lên: 07/08/2014, 07:21

... is devised, not for the Klyachko idempotent, but for rectangular- shaped q-Kostka numbers. On the other hand, q-Kostka numbers are defined in terms of Hall-Littlewood polynomials, and [9] shows ... = v(j) for all i, j.Awordw is said to be a shuffle of u and v if w has length r + s and if u and v are both subsequences of w. The shuffle product u ∃ v of u and v is an element of K...

Ngày tải lên: 07/08/2014, 08:22

... show that for some matrix M and for all vertices x and y,wehave M D (x, y) > 0 provided that for x = y,wehaveM(x, y)=0if(x, y) ∈ E(G). We will use the following fact from [4]. For the sake ... first non-trivial eigenvalue of the Laplacian and φ is the Perron vector of the transition probability matrix of a random walk on G. 1 Introduction For an undirected graph G on n ver...

Ngày tải lên: 07/08/2014, 13:21

... joining {v 2 ,v 3 ,v 4 } and {v 5 ,v 6 }.Fori =2, 3, 4, let N(v i ) \ N[v]={v  i }. Case 1. v  i = v  j for some i and j,where2≤ i<j≤ 4. We may assume that i =2 and j =3,andthatv 7 = v  2 .Ifv  4 = ... {v 5 ,v 6 } and {v 7 ,v 8 }. Since each of v 5 and v 6 is at distance 3 from a degree-4 vertex (namely, v 3 and v 4 ), d(v 5 )=d(v 6 ) = 3 by Observation 5. Further for...

Ngày tải lên: 07/08/2014, 13:21

... ∞. References [1] Madras N and Slade G 1993 The Self-Avoiding Walk (Boston: Birkh¨auser) [2] Hughes B D 1995 Random Walks and Random Environments, Vol I Random Walks (Oxford: Clarendon) [3] Vanderzande C 1998 ... of limit and sum is allowed: With n ∈ N and k ∈ N 0 let real numbers a n,k be given. Assume that lim n→∞ a n,k =: a k ∈ R for all k and that for all k there is a boun...

Ngày tải lên: 07/08/2014, 15:23

... perfect Hilbertian basis for the group of even signed permutations D n . Proof. By Theorem 3.3 and Remark 3.2, a, b and d are perfect bases for S n = G(1, 1, n), B n = G(2, 1, n) and D n = G(2, 2, n), ... index for D n which was introduced by Biagioli and Caselli [5]. the electronic journal of combinatorics 15 (2008), #R61 11 [5] R. Biagioli and F. Caselli, Invariant algebras...

Ngày tải lên: 07/08/2014, 15:23

... integer k and D/R ∞ is a chain. 3  : R ∞ = R k for some positive integer k and D/R ∞ is a regular directed tree with in-degree > 1 and out-degree 1 in the case  = − and with in-degree 1 and ... T − and D ∗ 2 is of the type T + . Finally, any cycle is of type NT and has properties 1 − and 1 + . Thus the (1 + , 1 − )-entries in the tables for all types T ± , T + , T...

Ngày tải lên: 07/08/2014, 21:21

... integer and let t 1 , . . . , t 2s , k 1 , . . . , k 2s and d be positive integers such that t j ≥ 3 and t j k j = 3d, for every j = 1, . . . , 2s. If each t j = 3 whenever d = 2 or 6 and if ... K 2w which lies in e 1 and label the vertices of K 2n+1 in such a way that ∞ /∈ V (K 2n+1 ). For each 2−factor F i , i = 1, . . . , w, let L i and M i be multisets of even and odd i...

Ngày tải lên: 08/08/2014, 14:22

... 1}.Inparticular (for H c = H i ), we get 74 Gerd Dethloff and Tran Van Tan n k) (t):=    v k) ϕ   ∩B(t) v k) ϕ υ for m ≥ 2, and n k) (t):=  |z|t v k) ϕ (z)form =1. Set N(r, v ϕ ):=N +∞) (r, v ϕ ). For ... to thank Professor Do Duc Thai for valuable discussions, the Universit´e de Bretagne Occidentale for its hospitality and support, and the PICS-CNRS For MathVietnam...

Ngày tải lên: 06/08/2014, 05:20