Lectures note combinators number thẻoy

... using this game. • How would you play this game? Computer Screen View • Note that we have dropped % from the payoff numbers. Illustration of Backward Induction in Senate Race Game: Gray’s Best ... win or lose). – Without loss of generality, assume the car is behind door number 1, and that there are goats behind door numbers 2 and 3. – Suppose you adopt the never switch strategy. The sa...

Ngày tải lên: 08/04/2014, 12:16

... sequentially. • Initially there are two piles of matches with a certain number of matches in each pile. • Players take turns removing any number of matches from a single pile. • The winner is the player ... gain/lose? Example 1: The merger game. Suppose an industry has six large firms (think airlines). Denote the largest firm as firm 1 and the smallest firm as firm 6. Suppose firm...

Ngày tải lên: 29/06/2014, 06:20

Ngày tải lên: 31/03/2014, 16:22

... colleagues in other factories have counted the total number of primes up to 10 20 .Weusu- ally write π(N ) to denote the number of primes up to the number N. Thus, the count I mentioned has given: π(10 8 ) ... maybedefinedasforthecasewhen R = Z. Noteworthy cases are when R is the ring of integers of a number field (for example, a quadratic number field), or R = Z[x] (or other 76 3. Pri...

Ngày tải lên: 31/03/2014, 16:22

... sets,J. Number Theory 68 (1998), 151–160. [6] P.J.Cameron,P.Erd˝os, On the number of sets of integers with various properties, in R. A. Mollin (ed.), Number Theory: Proc. First Conf. Can. Number ... +1−(k −)t)/2. Note that x(1) = ( +1)/2,x(t 2 )=2andx(t 1 )=1, where t 2 = k − 3 k −  ≥ 1andt 1 = k − 1 k −  . Furthermore, put H(x)= ln x x + x − 1 x ln x x − 1 . A note on the nu...

Ngày tải lên: 07/08/2014, 06:20

... ,|A + | and j =1, ,ρn. Denote this upper left block by M 1 . Also note that, similarly, M(i, j) = 1 for i = |A + | +1, ,m and j = ρn +1, ,2ρn.Denotethisblock M 2 .DenotebyM 3 the block consisting ... A note on the number of edges guaranteeing a C 4 in Eulerian bipartite digraphs Jian Shen Department of ... rows i = |A + |+1, ,m and the columns j =1, ,ρn.DenotebyM 4 the block consisting...

Ngày tải lên: 07/08/2014, 06:23

... Y ¯ 0 ¯ 0 T ¯ 1 T ¯ 0 T ¯ 0 T ¯ 0 T 0         the electronic journal of combinatorics 12 (2005), #N14 2 A Note on Two Multicolor Ramsey Numbers Alexander Engstr¨om ∗ Institute of Theoretical Computer Science ETH Z¨urich, ... new bounds for multicolor Ramsey numbers are proved: R(K 3 ,K 3 ,C 4 ,C 4 ) ≥ 27 and R 4 (C 4 ) ≤ 19. 1 Introduction We prove two new bounds for multicolor Rams...

Ngày tải lên: 07/08/2014, 08:22

... hence T − v are both transitive. the electronic journal of combinatorics 13 (2006), #N3 2 A Note on the Number of Hamiltonian Paths in Strong Tournaments Arthur H. Busch Department of Mathematics Lehigh ... 05C38 Abstract We prove that the minimum number of distinct hamiltonian paths in a strong tournament of order n is 5 n−1 3 . A known construction shows this number is best possible...

Ngày tải lên: 07/08/2014, 13:21

... graph. Counting the number of vertices in G n by rows from top to bottom, we see that the total number of vertices in G n is 2(1 + 2 + + n) + n + 1 = n(n + 1) + n + 1. Therefore, the number of edges ... small primes. Sometimes there is a compact formula for the number of mat chings, but it involves irrational numbers (for example, for the number of matchings of a rectangular grid-gr...

Ngày tải lên: 07/08/2014, 21:21

... pairwise distance greater than i. In this note we improve the upper b ound on the packing chromatic number of the square lattice. Keywords: Packing chromatic number, Packing colouring, Square lattice 1 ... combinatorial problems, the electronic journal of combinatorics 17 (2010), #N17 2 A note on packing chromatic number of the square lattice Roman Soukal ∗ Pˇremysl Holub † Submitted...

Ngày tải lên: 08/08/2014, 11:20