Báo cáo toán học: "Another Form of Matrix Nim" doc

... two dimensions of turning games in Chapter 14 of Winning Ways. 2. The Rules of the Game. In this paper, another form of matrix nim is proposed. This form is also a gen- eralization of Wythoff’s Game, ... positions of the form  ab cd  with a =min{a, b, c, d}. Then all L-positions are of the form, a + c<min{b, d}. (7) All R-positions are of the form, a + b<min...

Ngày tải lên: 07/08/2014, 06:23

... nihilation matrix K should satisfy L E K = 0, that is, the LHS and the nihilation matrix should not have common edges. Example. The left of Fig. 2 shows, in the form of a graph, the nihilation matrix of ... proper formalization of the functional notation L, p as a dot product. In addition, this new reformulation has led to the introduction of new concepts, like swaps (an a...

Ngày tải lên: 07/08/2014, 21:21

... smaller values of N(n): ∗ Sackler School of Mathematics and Blavatnik School of Computer Sciences, Tel Aviv University, Tel Aviv, Isra e l † Department of Compute r Science and Software Engineering, ... {u i , u j }.  We have found the proof of Theorem 1 during the 7th International Colloquium on Graph Theo r y in Hy`eres in September 2005. Another proof of the theorem was found,...

Ngày tải lên: 08/08/2014, 11:20

... and at least one of them contains an end of an edge of A  i ∩ B  since at least one of G[X i ∩ Y ] and G[X i ∩ Y ] contains an end of an edge of A i ∩ B. the electronic journal of combinatorics ... G ∗ is necessarily connected. Each bond of G is a circuit of G ∗ , and each circuit of G is a bond of G ∗ . If a theorem holds for a given set T of edges of G, then the...

Ngày tải lên: 08/08/2014, 11:20

Ngày tải lên: 05/08/2014, 09:46

... result of Kannan, Tetali and Vempala to com- pletely solve, via a simple proof, the problem of random generation of a labeled tournament with a given score vector. The proof uses the method of path ... score vector of a tournament is the sequence of out- degrees of the vertices of the tournament. In general, given a score vector with n scores, there can be an exponential (in n...

Ngày tải lên: 07/08/2014, 06:20

... sequence of types of the positions wi for i ≥ 1 (we think of this as the right phase diagram of w.) Proposition 4 The right phase diagram of w consists either of : • a string (possibly empty) of N ... which consists of the types of all the strings of the form awb where a, b > 0. We write this diagram as a quarter infinite array, with the value of a increasing upwards...

Ngày tải lên: 07/08/2014, 06:23

... member of the second coordinate of the label of y, delete the edge x j y.If the digit of z is 3 and y is not a member of the second coordinate of the label of z, delete the electronic journal of ... Subclaims, the proof of our lemma is complete. 5 Proof of the Main Theorem In this section, we present the proof of the main theorem. Let C be a topologically closed class o...

Ngày tải lên: 07/08/2014, 06:23

... 3) 2 +6 facets. Proof By Theorem 1.3 and the full dimensionality of DP(n) it follows that every facet of DP(n) is of the form x i ≥ x i+1 , for some i =1, ,n− 1 or of the form (3), for some 1 ... ×  n 2  incidence matrix of singletons vs. doubletons in [n], i.e., the rows of M(n) are indexed by [n] and the columns of M(n) (indexed by S(n)) are the characteristic vectors...

Ngày tải lên: 07/08/2014, 13:21

... an independent proof of the expression for F 1111 (n) used in the first proof. First proof This proof uses a procedure which, when successful, generates an incidence matrix uniformly at random ... Stirling numbers of the first and second kind respectively. As in the first proof, the number of pairs of preorders for which the meets of the blocks form a given k-partition of [n] is...

Ngày tải lên: 07/08/2014, 13:21