[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki7\/archives\/5262#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki7\/archives\/5262","headline":"\u30cd\u30c3\u30af\u30ec\u30b9\u591a\u9805\u5f0f – Wikipedia","name":"\u30cd\u30c3\u30af\u30ec\u30b9\u591a\u9805\u5f0f – Wikipedia","description":"\u7d44\u5408\u305b\u6570\u5b66\u306b\u304a\u3044\u3066\u3001\u30cd\u30c3\u30af\u30ec\u30b9\u591a\u9805\u5f0f (necklace polynomial) \u3042\u308b\u3044\u306f\uff08\u30e2\u30ed\u30fc (Moreau) \u306e\uff09\u30cd\u30c3\u30af\u30ec\u30b9\u6570\u3048\u4e0a\u3052\u95a2\u6570 (necklace-counting function) \u306f\u3001\u4ee5\u4e0b\u306e\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3088\u3046\u306a \u03b1 \u306e\u591a\u9805\u5f0f M (\u03b1, n) \u3067\u3042\u308b\u3002 \u03b1n=\u2211d\u2223ndM(\u03b1,d).{displaystyle alpha ^{n}=sum _{d,mid ,n}d,M(alpha","datePublished":"2020-01-30","dateModified":"2020-01-30","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki7\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki7\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/c7696cf455116ce8a1acab4c4e82c3b12143a7f2","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/c7696cf455116ce8a1acab4c4e82c3b12143a7f2","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki7\/archives\/5262","about":["Wiki"],"wordCount":1844,"articleBody":"\u7d44\u5408\u305b\u6570\u5b66\u306b\u304a\u3044\u3066\u3001\u30cd\u30c3\u30af\u30ec\u30b9\u591a\u9805\u5f0f (necklace polynomial) \u3042\u308b\u3044\u306f\uff08\u30e2\u30ed\u30fc (Moreau) \u306e\uff09\u30cd\u30c3\u30af\u30ec\u30b9\u6570\u3048\u4e0a\u3052\u95a2\u6570 (necklace-counting function) \u306f\u3001\u4ee5\u4e0b\u306e\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3088\u3046\u306a \u03b1 \u306e\u591a\u9805\u5f0f M (\u03b1, n) \u3067\u3042\u308b\u3002\u03b1n=\u2211d\u2223ndM(\u03b1,d).{displaystyle alpha ^{n}=sum _{d,mid ,n}d,M(alpha ,d).}  \u30e1\u30d3\u30a6\u30b9\u306e\u53cd\u8ee2\u516c\u5f0f\u306b\u3088\u3063\u3066\u3001\u30cd\u30c3\u30af\u30ec\u30b9\u591a\u9805\u5f0f\u306f  M(\u03b1,n)=1n\u2211d\u2223n\u03bc(nd)\u03b1d{displaystyle M(alpha ,n)={1 over n}sum _{d,mid ,n}mu left({n over d}right)alpha ^{d}}\u3068\u306a\u308b\u3002\u3053\u3053\u3067 \u03bc \u306f\u53e4\u5178\u7684\u306a\u30e1\u30d3\u30a6\u30b9\u95a2\u6570\u3067\u3042\u308b\u3002\u30cd\u30c3\u30af\u30ec\u30b9\u591a\u9805\u5f0f\u306f C. Moreau\u00a0(1872) \u306b\u3088\u3063\u3066\u7814\u7a76\u3055\u308c\u305f\u95a2\u6570\u3068\u5bc6\u63a5\u306a\u95a2\u4fc2\u306b\u3042\u308b\u304c\u3001\u540c\u3058\u3068\u3044\u3046\u308f\u3051\u3067\u306f\u306a\u3044\u3002\u30e2\u30ed\u30fc\u306f\u30cd\u30c3\u30af\u30ec\u30b9\u306e\u500b\u6570\u3092\u6570\u3048\u305f\u304c\u3001\u30cd\u30c3\u30af\u30ec\u30b9\u591a\u9805\u5f0f\u306f\u975e\u5468\u671f\u7684\u306a\u30cd\u30c3\u30af\u30ec\u30b9\u306e\u500b\u6570\u3092\u6570\u3048\u308b\u3002\u30cd\u30c3\u30af\u30ec\u30b9\u591a\u9805\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u73fe\u308c\u308b\u3002M (\u03b1, 1) = \u03b1M (\u03b1, 2) = (\u03b12 \u2212 \u03b1)\/2M (\u03b1, 3) = (\u03b13 \u2212 \u03b1)\/3M (\u03b1, 4) = (\u03b14 \u2212 \u03b12)\/4M (\u03b1, 5) = (\u03b15 \u2212 \u03b1)\/5M (\u03b1, 6) = (\u03b16 \u2212 \u03b13 \u2212 \u03b12 + \u03b1)\/6M (\u03b1, pn) = (\u03b1pn \u2212 \u03b1pn \u2212 1)\/pn,\u3000\u305f\u3060\u3057 p \u306f\u7d20\u6570\u3002(i, j\u2009) \u3092 i \u3068 j \u306e\u6700\u5927\u516c\u7d04\u6570\u3001[i, j\u2009] \u3092 i \u3068 j \u306e\u6700\u5c0f\u516c\u500d\u6570\u3068\u3057\u3066\u3001  M(\u03b1\u03b2,n)=\u2211[i,j]=n(i,j)M(\u03b1,i)M(\u03b2,j).{displaystyle M(alpha beta ,n)=sum _{[i,j]=n}(i,j)M(alpha ,i)M(beta ,j).}\u3000\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]^ a b Lothaire, M. (1997). Combinatorics on words. Encyclopedia of Mathematics and Its Applications. 17. Perrin, D.; Reutenauer, C.; Berstel, J.; Pin, J. E.; Pirillo, G.; Foata, D.; Sakarovitch, J.; Simon, I.; Sch\u00fctzenberger, M. P.; Choffrut, C.; Cori, R.; Lyndon, Roger; Rota, Gian-Carlo. Foreword by Roger Lyndon (2nd ed.). Cambridge University Press. pp.\u00a079,84. ISBN\u00a00-521-59924-5. MR1475463. Zbl\u00a00874.20040\u00a0Moreau, C. (1872), \u201cSur les permutations circulaires distinctes (On distinct circular permutations)\u201d (French), Nouvelles annales de math\u00e9matiques, journal des candidats aux \u00e9coles polytechnique et normale, S\u00e9r. 2 11:  309\u201331, JFM\u00a004.0086.01, http:\/\/www.numdam.org\/item?id=NAM_1872_2_11__309_0\u00a0Metropolis, N.; Rota, Gian-Carlo (1983), \u201cWitt vectors and the algebra of necklaces\u201d, Advances in Mathematics 50 (2):  95\u2013125, doi:10.1016\/0001-8708(83)90035-X, ISSN\u00a00001-8708, MR723197, Zbl\u00a00545.05009\u00a0"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki7\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki7\/archives\/5262#breadcrumbitem","name":"\u30cd\u30c3\u30af\u30ec\u30b9\u591a\u9805\u5f0f – Wikipedia"}}]}]