翻訳と辞書 Words near each other ・ Lattice gauge theory ・ Lattice girder ・ Lattice graph ・ Lattice Group ・ Lattice group ・ Lattice light-sheet microscopy ・ Lattice mast ・ Lattice Miner ・ Lattice model ・ Lattice model (biophysics) ・ Lattice model (finance) ・ Lattice model (physics) ・ Lattice multiplication ・ Lattice networks ・ Lattice of subgroups ・ Lattice path ・ Lattice phase equaliser ・ Lattice plane ・ Lattice problem ・ Lattice protein ・ Lattice QCD ・ Lattice reduction ・ Lattice scattering ・ Lattice Semiconductor ・ Lattice sieving ・ Lattice stool ・ Lattice tower ・ Lattice truss bridge ・ Lattice word ・ Lattice-based access control Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Lattice path ： ウィキペディア英語版 Lattice path In combinatorics, a lattice path $L$ in $\backslash mathbb^d$ of length $k$ with steps in $S$ is a sequence $v\_0,\; v\_1,\; \backslash ldots,\; v\_k\; \backslash in\; \backslash mathbb^d$ such that each consecutive difference $v\_i\; -\; v\_$ lies in $S$. A lattice path may lie in any lattice in $\backslash mathbb^d$,〔 but the integer lattice $\backslash mathbb^d$ is most commonly used. An example of a lattice path in $\backslash mathbb^2$ of length 5 with steps in $S\; =\; \backslash lbrace\; (2,0),\; (1,1),\; (0,-1)\; \backslash rbrace$ is $L\; =\; \backslash lbrace\; (-1,-2),\; (0,-1),\; (2,-1),\; (2,-2),\; (2,-3),\; (4,-3)\; \backslash rbrace$. ==North-East lattice paths== A North-East (NE) lattice path is a lattice path in $\backslash mathbb^2$ with steps in $S\; =\; \backslash lbrace\; (0,1),\; (1,0)\; \backslash rbrace$. The $(0,1)$ steps are called North steps and denoted by $N$'s; the $(1,0)$ steps are called East steps and denoted by $E$'s. NE lattice paths most commonly begin at the origin. This convention allows us to encode all the information about a NE lattice path $L$ in a single permutation word. The length of the word gives us the number of steps of the lattice path, $k$. The order of the $N$'s and $E$'s communicates the sequence of $L$. Furthermore, the number of $N$'s and the number of $E$'s in the word determines the end point of $L$. If the permutation word for a NE lattice path contains $n$ $N$steps and $e$ $E$ steps, and if the path begins at the origin, then the path necessarily ends at $(e,n)$. This follows because you have "walked" exactly $n$ steps North and $e$ steps East from $(0,0)$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lattice path」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.