18,867 research outputs found

    An explicit universal cycle for the (n-1)-permutations of an n-set

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    We show how to construct an explicit Hamilton cycle in the directed Cayley graph Cay({\sigma_n, sigma_{n-1}} : \mathbb{S}_n), where \sigma_k = (1 2 >... k). The existence of such cycles was shown by Jackson (Discrete Mathematics, 149 (1996) 123-129) but the proof only shows that a certain directed graph is Eulerian, and Knuth (Volume 4 Fascicle 2, Generating All Tuples and Permutations (2005)) asks for an explicit construction. We show that a simple recursion describes our Hamilton cycle and that the cycle can be generated by an iterative algorithm that uses O(n) space. Moreover, the algorithm produces each successive edge of the cycle in constant time; such algorithms are said to be loopless

    Investment specificity, vertical integration and market foreclosure

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    In this paper we consider the impact of vertical integration on a retailer's choices of product variety and specific, brand-supporting investment. In an incomplete contract environment, vertical merger encourages investment in integrated supply, and foreclosure of non-integrated manufacturers. Anti-competitive as opposed to efficiency interpretations depend delicately on a trade-off between the benefits of supplier-specific rather than generally applicable retailer investment, and the value of multi-product rather than single product retailing. Where retailers compete, it is shown that vertical integration implements competition reducing, product differentiating investment strategies.incomplete contracts,vertical integration,monopolization

    Are There Differential Effects of Price and Policy on College Students' Drinking Intensity?

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    This paper investigates whether college students' response to alcohol price and policies differ according to their drinking intensity. Individual level data on drinking behavior, price paid per drink, and college alcohol policies come from the student and administrator components of the 1997 and 1999 waves of the Harvard School of Public Health (HSPH) College Alcohol Study (CAS). Students drinking behavior is classified on the basis of the number of drinks they typically consume on a drinking occasion, and the number of times they have been drunk during the 30 days prior to survey. A generalized ordered logit model is used to determine whether key variables impact differentially the odds of drinking and the odds of heavy drinking. We find that students who faced a higher money price for alcohol are less likely to make the transition from abstainer to moderate drinker and moderate drinker to heavy drinker, and this effect is equal across thresholds. Campus bans on the use of alcohol are a greater deterrent to moving from abstainer to moderate drinker than moderate drinker to heavy drinker.
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