Shuffle operations on discrete paths

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• 作者：S. Brlek ; G. Labelle ; A. Lacasse
• 关键词：Lattice paths ; Polygonal paths ; Discrete regions ; Shuffle ; Dragon curve
• 刊名：Theoretical Computer Science
• 出版年：2008
• 出版时间：4 February 2008
• 年：2008
• 卷：391
• 期：1-2
• 页码：75-89
• 全文大小：653 K

文摘

We consider the shuffle operation on paths and study some parameters. In the case of square lattices, shuffling with a particular periodic word (of period 2) corresponding to paperfoldings reveals some characteristic properties: closed paths remain closed; the area and perimeter double; the center of gravity moves under a 45 rotation and a cache/MiamiImageURL/B6V1G-4PYYTYC-1-2/0?wchp=dGLbVtb-zSkzk"" alt=""Click to view the MathML source"" align=""absbottom"" border=""0"" height=15 width=21> zoom factor. We also observe invariance properties for the associated Dragon curves. Moreover, replacing square lattice paths by paths involving 2kπ/N-turns, we find analogous results using more general shuffles.