منابع مشابه
No Dice Theorem on Symmetric Cones
The monotonicity of the least squares mean on the Riemannian manifold of positive definite matrices, conjectured by Bhatia and Holbrook and one of key axiomatic properties of matrix geometric means, was recently established based on the Strong Law of Large Number [14, 4]. A natural question concerned with the S.L.L.N is so called the no dice conjecture. It is a problem to make a construction of...
متن کاملTied dice
A generalized die is a list (x1; :::; xn) of integers. For integers n 1, a b and s let D(n; a; b; s) be the set of all dice with a x1 ::: xn b and P xi = s. Two dice X and Y are tied if the number of pairs (i; j) with xi < yj equals the number of pairs (i; j) with xi > yj . We prove the following: with one exception (unique up to isomorphism), if X 6= Y 2 D(n; a; b; s) are tied dice neither of ...
متن کاملDice graphs
For integers n 1, a b and s let D(n; a; b; s) be the set of all lists of integers (x1; :::; xn) with a x1 ::: xn b and P xi = s. There is a graph G(n; a; b; s) with vertex-set D(n; a; b; s) in which two vertices are adjacent if one is stronger than the other in a natural dice game. In The prevalence of paradoxical dice [Bull. Inst. Combin. Appl. 45 (2005), 70-76] the dice which are isolated v...
متن کاملA Game of Nontransitive Dice
We consider a two player simultaneous-move game where the two players each select any permissible n-sided die for a fixed integer n. A player wins if the outcome of his roll is greater than that of his opponent. Remarkably, for n > 3, there is a unique Nash Equilibrium in pure strategies. The unique Nash Equilibrium is for each player to throw the Standard n-sided die, where each side has a dif...
متن کاملSicherman Dice
The subject of Sicherman dice began with a question posed and answered by Colonel George Sicherman which was originally reported in the February 1978 issue of Scientific American. Sicherman wanted to determine if there was another way to label a pair of sixsided dice, using only positive integers such that the probabilities of the sums would be the same as a standard dice. Sicherman discovered ...
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ژورنال
عنوان ژورنال: Derecho Animal. Forum of Animal Law Studies
سال: 2016
ISSN: 2462-7518
DOI: 10.5565/rev/da.321