翻訳と辞書 Words near each other ・ Necker–Sharpe Funeral Home ・ Necking ・ Necking (engineering) ・ Necklace ・ Necklace (combinatorics) ・ Necklace (disambiguation) ・ Necklace and Calabash ・ Necklace carpetshark ・ Necklace fern ・ Necklace Nebula ・ Necklace of Harmonia ・ Necklace of Precious Pearls ・ Necklace of the Stars ・ Necklace of Venus ・ Necklace pipistrelle ・ Necklace polynomial ・ Necklace problem ・ Necklace ring ・ Necklace Road ・ Necklace Road railway station ・ Necklace splitting problem ・ Necklaced spinetail ・ Necklacing ・ Neckline ・ Necks ・ Necks (EP) ・ Necktie ・ Necktie paradox ・ Necktie River ・ Necktie Second 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 Necklace polynomial ： ウィキペディア英語版 Necklace polynomial In combinatorial mathematics, the necklace polynomials, or (Moreau's) necklace-counting function are the polynomials in ''α'' such that :$\backslash alpha^n\; =\; \backslash sum\_\; d\; \backslash ,\; M(\backslash alpha,\; d).$ By Möbius inversion they are given by : $M(\backslash alpha,n)\; =\; \backslash sum\_\backslash mu\backslash left(\backslash right)\backslash alpha^d$ where is the classic Möbius function. The necklace polynomials are closely related to the functions studied by , though they are not quite the same: Moreau counted the number of necklaces, while necklace polynomials count the number of aperiodic necklaces. The necklace polynomials appear as: * the number of aperiodic necklaces (also called Lyndon words) that can be made by arranging beads the color of each of which is chosen from a list of colors (One respect in which the word "necklace" may be misleading is that if one picks such a necklace up off the table and turns it over, thus reversing the roles of clockwise and counterclockwise, one gets a different necklace, counted separately, unless the necklace is symmetric under such reflections.); * the dimension of the degree piece of the free Lie algebra on generators ("Witt's formula"); * the number of monic irreducible polynomials of degree over a finite field with elements (when is a prime power); * the exponent in the cyclotomic identity; *The number of Lyndon words of length ''n'' in an alphabet of size α.〔 ==Values== : $$ \begin M(1,n) & = 0 \textn>1 \\ M(\alpha,1) & =\alpha \\() M(\alpha,2) & =(\alpha^2-\alpha)/2 \\() M(\alpha,3) & =(\alpha^3-\alpha)/3 \\() M(\alpha,4) & =(\alpha^4-\alpha^2)/4 \\() M(\alpha,5) & =(\alpha^5-\alpha)/5 \\() M(\alpha,6) & =(\alpha^6-\alpha^3-\alpha^2+\alpha)/6 \\() M(\alpha,p^N) & =(\alpha^-\alpha^p\text \\() M(\alpha\beta, n) & =\sum_ \gcd(i,j)M(\alpha,i)M(\beta,j) \end :: where "gcd" is greatest common divisor and "lcm" is least common multiple. 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「Necklace polynomial」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.