Báo cáo toán học: "Dynamic One-Pile Blocking Nim" potx

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Ngày tải lên: 05/08/2014, 15:20

... independent computations of the number of Latin squares of order 10. We also give counts of Latin rectangles with up to 10 columns, and estimates of the number of Latin squares of orders up to 15. Mathematics ... subgraph of degree one. A one-factorization of G is a partition of E(G) into one-factors. Clearly, the rows of a Latin rectangle R correspond to the one-fac...

Ngày tải lên: 07/08/2014, 06:20

... S of subsets of a finite set S whose union is S is connected if and only if there is an evolutionary path in S between any two members of S. Proof:IfS is a finite connected family of subsets of ... the members of i S [S] account for at least five of the seven nonempty subsets of S. Without losing generality we may assume that the complement in P(S) − {∅} of i S [S] is a subset...

Ngày tải lên: 07/08/2014, 06:20

... August 3, 2000 Abstract Let d(n) count the lattice paths from (0, 0) to (n, n) using the steps (0,1), (1,0), and (1,1). Let e(n) count the lattice paths from (0, 0) to (n, n)with permitted steps ... of lattice paths defined on various sets of permitted steps which yield path counts related to the Narayana polynomials. Mathematical Reviews Subject Classification: 05A15 Key words: La...

Ngày tải lên: 07/08/2014, 06:20

... graph as a planar embedding of a maximal hypergraph such that the faces of the graph correspond to the edges of the hypergraph. 3 Colouring planar mixed hypergraphs Let H =(V,C, D) be a mixed hypergraph. ... colouring properties of general planar mixed hypergraphs was first raised in [13] (problem 8, p.43). It is evident that every planar D-hypergraph is colourable, just as every...

Ngày tải lên: 07/08/2014, 06:22

... combinatorics 10 (2003), #N4 1 suggest that the structure of the Dynamic One-pile Blocking Nim may be not effected by the introduction of blocking- options of the opponent — what is proved in this article. This ... Dynamic One-Pile Blocking Nim Achim Flammenkamp Mathematisierung, Universităat Bielefeld, Federal Republic of ... be forced by the blocking move of his opponent to reduc...

Ngày tải lên: 07/08/2014, 07:21

... chromatically unique if a k <a 1 + a 2 , and find examples showing that θ(a 1 ,a 2 , ···,a k )maynotbe chromatically unique if a k = a 1 + a 2 . Keywords: Chromatic polynomials, χ -unique, χ-closed, ... θ(a 1 ,a 2 , ···,a k ) is χ -unique if a i ≥ k − 1 for i = 1, 2, ···,k. ✷ Theorem 2.3 ([11]) Let h ≥ s +1≥ 2 or s = h +1. Then for k ≥ 5, θ(a 1 ,a 2 , ···,a k ) is χ -unique if a 2 − 1...

Ngày tải lên: 07/08/2014, 08:20

... Reiter, Nimlike Games with Generalized Bases, Rocky Moun- tain Journal of Mathematics,toappear. the electronic journal of combinatorics 13 (2006), #N7 7 Dynamic Single-Pile Nim Using Multiple ... and H. Reiter, Dynamic One-Pile Blocking Nim, Electronic Journal of Combinatorics, Volume 10(1), 2003, #N4. [5] Holshouser, A., and H. Reiter, One Pile Nim with Arbitrary Move Function, E...

Ngày tải lên: 07/08/2014, 13:21

... d, and p i > p j . In particular, 1 -descents correspond to descents in the traditional sense, and (n − 1) -descents correspond to inversions. This concept was introduced in [2] by De Mari and ... Y n,k and the vertices of G, and 2. If V 1 and V 2 are two disjoint sets of vertices of G so that no edge of G has one end- point in V 1 and another one in V 2 , then the corres...

Ngày tải lên: 07/08/2014, 15:22

... general problem that we solve, the “coupon collector’s problem with quotas,” is for a payoff word with letters in the set L which appear with probabilities p = p  :  ∈ L and quotas q = q  : ... journal of combinatorics 15 (2008), #N31 5 with a uniform distribution of the coupons. Wilf and Myers in [3] re-derived the result of Newman and Shepp, but with a generating function...

Ngày tải lên: 07/08/2014, 15:22

... image partition regular if given any pair (S, A), M is image partition regular over S with respect to A. In the following discussions we shall observe that for matrices of finite order image partition ... In this paper we introduce a new notion which we call universally image partition regular matrices, which are in fact image partition regular over all semigroups and every...

Ngày tải lên: 07/08/2014, 21:21

... 2 Proofs The multiplicative magic squares can be described in terms of the additive ones in the following way: We write n A for the multiplicative magic square given by n A = n A(i,j) 1i,jr . If ... additive -multiplicative magic squares of order r = 5 with distinct entries? We have seen that the answer is negative for r = 4. On the contrary, Horner [4] found an additive and mul...

Ngày tải lên: 08/08/2014, 01:20

... local ring of V S ⊂ A n is of homogeneous type, then its extensions will a l s o have local rings of homogeneous type if and only if ℓ ≤ ∆(m). Proof. Let K[[S]] denote the local ring of V S , i.e. ... consider extensions of a toric variety whose local ring has a non-decreasing Hilbert function and whose tangent cone is not necessarily Cohen-Macaulay. The proof is a modification of...

Ngày tải lên: 08/08/2014, 14:23

... journal of combinatorics 18 (2011), #P97 2 Two Characterizations of Hypercubes Juhani Nieminen, Matti Peltola and Pasi Ruotsalainen Department of Mathematics, University of Oulu University of Oulu, ... vertex of G has degree n i.e. G is regular of degree n. Claim 3.The graph G is bipartite. Proof of C l aim 3. If a prime convex P i cuts off an edge of a cycle it must cut o...

Ngày tải lên: 08/08/2014, 14:23

... in particular not on a variation of Wythoff Nim. (if we drop the ‘upper’ condition then one may obvi ously regard the P -positions of, for example, Wythoff Nim as a splitting sequence, see [Lar2]). At ... forbidden options.) Let us recall some other blocking variations o f Wythoff Nim. Definition 9. Le t k ∈ N. In the game of k-blocking Wythoff Nim [HeLa06, Lar09, FrPe], the blockin...

Ngày tải lên: 08/08/2014, 14:23