Zipf's Law, Hierarchical Structure, and Cards-Shuffling Model for Urban Development
نویسندگان
چکیده
منابع مشابه
Cards-Shuffling Model for Urban Development
Hierarchy of cities reflects the ubiquitous structure frequently observed in the natural world and social institutions. Where there is a hierarchy with cascade structure, there is a Zipf’s rank-size distribution, and vice versa. However, we have no theory to explain the spatial dynamics associated with Zipf’s law of cities. In this paper, a new angle of view is proposed to find the simple rules...
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We consider a problem of shuffling a deck of cards with ordered labels. Namely we split the deck of N = kq cards (where t ≥ 1 is maximal) into k equally sized stacks and then take the top card off of each stack and sort them by the order of their labels and add them to the shuffled stack. We show how to find stacks of cards invariant and periodic under the shuffling. We also show when gcd(q, k)...
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Abstract Two notions of riffle shuffling on finite Coxeter groups are given: one using Solomon’s descent algebra and another using random walk on chambers of hyperplane arrangements. These definitions coincide for types A,B,H3, and rank two groups. Both notions satisfy a convolution property and have the same simple eigenvalues. The hyperplane definition is especially natural and satisfies a po...
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This paper is about the following question: How many riffle shuffles mix a deck of card for games such as blackjack and bridge? An object that comes up in answering this question is the descent polynomial associated with pairs of decks, where the decks are allowed to have repeated cards. We prove that the problem of computing the descent polynomial given a pair of decks is #P -complete. We also...
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ژورنال
عنوان ژورنال: Discrete Dynamics in Nature and Society
سال: 2012
ISSN: 1026-0226,1607-887X
DOI: 10.1155/2012/480196