منابع مشابه
Covering a chessboard with staircase walks
An ascending (resp., descending) staircase walk on a chessboard is a rook’s path that goes either right or up (resp., down) in each step. We show that the minimum number of staircase walks that together visit every square of an n× n chessboard is d 3ne .
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Let C(n,m) be a n×m chessboard. An ascending (respectively descending) staircasewalk on C(n,m) is a rook’s path on C(n,m) that in every step goes either right or up (respectively right or down). We determine the minimal number of ascending and descending staircase walks covering C(n,m). © 2015 Elsevier B.V. All rights reserved.
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Staircase walks are lattice paths from to which take diagonal steps and which never fall below the -axis. A path hitting the -axis times is assigned a weight of where . A simple local Markov chain which connects the state space and converges to the Gibbs measure (which normalizes these weights) is known to be rapidly mixing when , and can easily be shown to be rapidly mixing when . We give the ...
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We analyze a deterministic form of the random walk on the integer line called the liar machine, similar to the rotor-router model, finding asymptotically tight pointwise and interval discrepancy bounds versus random walk. This provides an improvement in the best-known winning strategies in the binary symmetric pathological liar game with a linear fraction of responses allowed to be lies. Equiva...
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The first crystal structure of a ring helicase encircling single-stranded DNA reveals a mechanism for ATP-dependent DNA translocation.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2013.07.017