منابع مشابه
Tied 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 کاملConcerning Dice and Divinity
Einstein initially objected to the probabilistic aspect of quantum mechanics— the idea that God is playing at dice. Later he changed his ground, and focussed instead on the point that the Copenhagen Interpretation leads to what Einstein saw as the abandonment of physical realism. We argue here that Einstein's initial intuition was perfectly sound, and that it is precisely the fact that quantum ...
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 ...
متن کاملInstructor : Nikhil Bansal Scribe :
In this lecture we will be looking into the secretary problem, and an interesting variation of the problem called the incentive comparable secretary problem. For both of these problems we will show how they can be solved though a correspondence between all possible strategies and the feasible solution space to a linear program. In both cases this will allow us to derive an algorithm and prove t...
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ژورنال
عنوان ژورنال: III-Vs Review
سال: 2006
ISSN: 0961-1290
DOI: 10.1016/s0961-1290(06)71638-6