منابع مشابه
Shuffling with ordered cards
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)...
متن کاملShuffling Cards and Stopping Times
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متن کاملCards-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...
متن کاملDescent Algebras , Hyperplane Arrangements , and Shuffling Cards
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...
متن کاملDescent algebras, hyperplane arrangements, and shuffling cards. To appear
This note establishes a connection between Solomon’s descent algebras and the theory of hyperplane arrangements. It is shown that card-shuffling measures on Coxeter groups, originally defined in terms of descent algebras, have an elegant combinatorial description in terms of random walk on the chambers of hyperplane arrangements. As a corollary, a positivity conjecture of Fulman is proved.
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2010
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2010.v1.n2.a3