{"id":26281,"date":"2021-05-15T13:02:05","date_gmt":"2021-05-15T05:02:05","guid":{"rendered":"https:\/\/swarma.org\/?p=26281"},"modified":"2021-05-15T13:02:05","modified_gmt":"2021-05-15T05:02:05","slug":"%e4%bb%80%e4%b9%88%e6%98%af%e8%b6%85%e5%9b%be-%e9%9b%86%e6%99%ba%e7%99%be%e7%a7%91","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=26281","title":{"rendered":"\u4ec0\u4e48\u662f\u8d85\u56fe | \u96c6\u667a\u767e\u79d1"},"content":{"rendered":"
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\uff08\u6570\u5b66\u4e2d\u8457\u540d\u7684 Erdos number \u7f51\u7edc\u662f\u666e\u901a\u56fe\uff0c\u901a\u8fc7\u8fde\u8fb9\u6211\u4eec\u53ef\u4ee5\u770b\u5230 Erdos \u6216\u5176\u4ed6\u6570\u5b66\u5bb6\u4e4b\u95f4\u7684\u5408\u4f5c\uff0c\u4f46\u662f\u65e0\u6cd5\u770b\u5230\u4e09\u4e2a\u6216\u4e09\u4e2a\u4ee5\u4e0a\u6570\u5b66\u5bb6\u4e4b\u95f4\u7684\u5408\u4f5c\u5173\u7cfb\u3002\u5373\u4f7f\u8fde\u63a5\u591a\u4e2a\u6570\u5b66\u5bb6\u8282\u70b9\u4e5f\u4ec5\u4ee3\u8868\u4e24\u4e24\u4e4b\u95f4\u6709\u8fc7\u5408\u4f5c\u800c\u975e\u6709\u8fc7\u5171\u540c\u5408\u4f5c\uff09<\/span><\/p>\n

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\u56e0\u6b64\u6570\u5b66\u5bb6 Berge \u4e8e20\u4e16\u7eaa60\u5e74\u4ee3\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684\u56fe\u7406\u8bba\uff1a\u4ee5\u4f5c\u8005\u4e3a\u8282\u70b9\uff0c\u4ee5\u6210\u679c\u4e3a\u8fb9\u96c6\uff0c\u5b8c\u7f8e\u63cf\u8ff0\u4e86\u8be5\u7c7b\u7f51\u7edc\u7279\u6027\uff0c\u8fd9\u5c31\u662f\u8d85\u56fe\uff08Hypergraph\uff09\uff0c\u6216\u79f0\u4e3a\u65e0\u5411\u8d85\u56fe\u3002\u968f\u540e\u6709\u5b66\u8005\u5bf9\u6709\u5411\u8d85\u56fe\u7406\u8bba\u3001\u8d85\u56fe\u7684\u8d85\u56de\u8def\u3001\u7740\u8272\u548ct-\u8bbe\u8ba1\uff08t-design\uff09\u7b49\u65b9\u9762\u8fdb\u884c\u4e86\u7814\u7a76\u3002<\/span><\/p>\n

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\u8d85\u56feH\u662f\u4e00\u4e2a\u6709\u5e8f\u4e8c\u5143\u7ec4 H=(X,E)\uff0c \u5176\u4e2dX\u662f\u4e00\u4e2a\u4ee5\u8282\u70b9\u6216\u9876\u70b9\uff08vertices\uff09\u4e3a\u5143\u7d20\u7684\u975e\u7a7a\u96c6\u5408\uff0c\u79f0\u4e3a\u9876\u70b9\u96c6\uff1bE\u662fX\u7684\u4e00\u7ec4\u975e\u7a7a\u5b50\u96c6\u7c07\uff0c\u5176\u5143\u7d20\u88ab\u79f0\u4e3a\u8fb9\u6216\u8d85\u8fb9\u3002<\/span><\/p>\n<\/blockquote>\n

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\u56e0\u6b64\uff0c\u82e5P(X)\u662fX\u7684\u5e42\u96c6\uff0c\u5219E\u662f P(X)\u2216{\u2205} \u7684\u4e00\u4e2a\u5b50\u96c6\u3002\u5728\u8d85\u56feH\u4e2d\uff0c\u9876\u70b9\u96c6\u7684\u5927\u5c0f\u88ab\u79f0\u4e3a\u8d85\u56fe\u7684\u9636\u6570\uff08order of the hypergraph\uff09\uff0c\u8fb9\u96c6\u7684\u5927\u5c0f\u88ab\u79f0\u4e3a\u8d85\u56fe\u7684\u5927\u5c0f\uff08size of the hypergraph\uff09\u3002<\/span><\/p>\n

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\u8d85\u56fe\u6709\u8bb8\u591a\u79cd\uff0c\u5176\u4e2d\u6709\u4e00\u79cd\u53eb\u505ak-\u5300\u9f50\u8d85\u56fe\uff08k-uniform hypergraph\uff0c\u6216\u8bd1\u4f5ck-\u4e00\u81f4\u8d85\u56fe\uff09\u3002\u5b83\u6307\u6bcf\u4e2a\u8fb9\u8fde\u63a5\u7684\u9876\u70b9\u6570\u90fd\u76f8\u540c\u4e14\u7b49\u4e8ek\u7684\u8d85\u56fe\u3002\u56e0\u6b642-\u5300\u9f50\u8d85\u56fe\u5c31\u662f\u4f20\u7edf\u610f\u4e49\u4e0a\u7684\u56fe\u5373\u201c\u666e\u901a\u56fe\u201d\uff0c\u7814\u7a76\u666e\u901a\u56fe\u7684\u56fe\u8bba\u4e3a\u201c\u4f20\u7edf\u56fe\u8bba\u201d\uff0c\u7814\u7a763-\u5300\u9f50\u8d85\u56fe\u4ee5\u4e0a\u4e09\u5143\u6216\u591a\u5143\u7ec4\u7684\u96c6\u5408\u7684\u5373\u4e3a\u8d85\u56fe\u7406\u8bba\u3002<\/span><\/p>\n<\/section>\n

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\u8d85\u56fe\u662f\u6709\u9650\u96c6\u5408\u7684\u5b50\u96c6\u7cfb\u7edf\uff0c\u662f\u79bb\u6563\u6570\u5b66\u4e2d\u6700\u4e00\u822c\u7684\u7ed3\u6784\u3002\u65e9\u671f\u7ecf\u5178\u7684\u5b9a\u7406\u6709Sperner\u5b9a\u7406\u548cRamsey\u5b9a\u7406\u7b49\u3002\u65e2\u7136\u201c\u8d85\u56fe\u201d\u662f\u666e\u901a\u56fe\u7684\u63a8\u5e7f\uff0c\u57fa\u672c\u6982\u5ff5\u548c\u5b9a\u4e49\u90fd\u662f\u56fe\u7684\u76f8\u5e94\u6982\u5ff5\u548c\u5b9a\u4e49\u7684\u5e73\u79fb\u548c\u63a8\u5e7f\uff0c\u8fd9\u65b9\u9762\u5df2\u53d6\u5f97\u4e86\u4e00\u4e9b\u91cd\u8981\u7ed3\u679c\uff0c\u5982 Erd\u00f6s-Ko-Rado\u5b9a\u7406\u7b49\u3002Berge \u5199\u4e86\u4e00\u672c\u4e13\u8457\u201cHypergraphs\u201d\u5bf9\u5176\u505a\u4e86\u7cfb\u7edf\u7684\u603b\u7ed3\u3002<\/span><\/section>\n
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\u6c11\u4ee5\u98df\u4e3a\u5929\uff0c\u5b9a\u83dc\u8c31\u662f\u5bb6\u5bb6\u6237\u6237\u6bcf\u5929\u90fd\u8981\u9047\u5230\u7684\u5b9e\u9645\u95ee\u9898\u3002\u4e3a\u4e86\u5065\u5eb7\uff0c\u73b0\u4ee3\u4eba\u8bb2\u7a76\u8425\u517b\u591a\u6837\u5316\uff0c\u6240\u4ee5\u6bcf\u5929\u8981\u4f7f\u7528\u4e0d\u540c\u7684\u83dc\u8c31\u3002\u73b0\u5728\u6211\u4eec\u6709\u5982\u4e0b\u5341\u4e94\u79cd\u852c\u83dc\uff0c\u6bcf\u4e2a\u83dc\u8c31\u4ece\u8fd9\u5341\u4e94\u79cd\u91cc\u9009\u53d6\u4e00\u90e8\u5206\uff1a\u767d\u83dc\u3001\u841d\u535c\u3001\u80e1\u841d\u535c\u3001\u9752\u6912\u3001\u9ec4\u74dc\u3001\u82e6\u74dc\u3001\u897f\u846b\u82a6\u3001\u897f\u7ea2\u67ff\u3001\u83b4\u82e3\u3001\u83e0\u83dc\u3001\u9752\u83dc\u3001\u8304\u5b50\u3001\u6d0b\u8471\u3001\u97ed\u83dc\u3001\u897f\u5170\u82b1\u3002\u4e00\u4e2a\u6708\u5185\u6bcf\u79cd\u852c\u83dc\u6211\u4eec\u90fd\u4f7f\u7528\u8fc7\uff0c\u5373\u4e09\u5341\u4e2a\u83dc\u8c31\u6709\u4e09\u5341\u6761\u8fb9\uff08\u5373\u201c\u8d85\u8fb9\u201d\uff0c\u540e\u6587\u4e00\u5f8b\u79f0\u4e3a\u201c\u8fb9\u201d\uff09\uff0c\u5f62\u6210\u4e86\u5728\u5341\u4e94\u79cd\u852c\u83dc\u4e0a\u7684\u8d85\u56fe\u3002\u90a3\u4e48\u95ee\u9898\u6765\u4e86\uff1a\u4f7f\u7528\u8fd9\u5341\u4e94\u79cd\u852c\u83dc\uff0c\u6700\u591a\u80fd\u505a\u51fa\u591a\u5c11\u4e2a\u4e0d\u540c\u7684\u83dc\u8c31\uff1f<\/span><\/section>\n

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\u6839\u636e Sperner\u5b9a\u7406\uff0c\u8fd9\u4e2a\u6570\u662f\u4e0d\u8d85\u8fc7<\/span>\u7684\u3002\u4e0a\u56fe\u7684\u5706\u62ec\u53f7\u5c31\u662f\u6211\u4eec\u9ad8\u4e2d\u5b66\u8fc7\u7684\u201c\u7ec4\u5408\u201d\u7684\u610f\u601d\uff0c\u6ce8\u610fn\/2\u5916\u7684\u534a\u4e2a\u65b9\u62ec\u53f7\u662f\u201c\u53d6\u6574\u201d\u7684\u610f\u601d\u3002\u6240\u4ee5\u5728\u8fd9n=15\u79cd\u852c\u83dc\u96c6\u5408\u4e0a\u7684\u7b80\u5355\u8d85\u56fe\uff0c\u5176\u8fb9\u6570\u6700\u591a\u4e3a6435\u6761\u3002\u8fd9\u91cc\u7b80\u5355\u8d85\u56fe\uff08Simple hypergraph\uff09\u7684\u6982\u5ff5\u5f88\u91cd\u8981\uff0c\u5b83\u4f5c\u4e3a\u8d85\u56fe\u4efb\u610f\u4e24\u6761\u8fb9\u90fd\u4e92\u4e0d\u5305\u542b\u3002\u6bd4\u5982\u4f60\u4e0d\u53ef\u4ee5\u4e00\u5929\u7684\u83dc\u8c31\u5b9a\u4e3a\uff08\u9752\u83dc\uff0c\u841d\u535c\uff09\uff0c\u53e6\u4e00\u5929\u7684\u83dc\u8c31\u5b9a\u4e3a\uff08\u9752\u83dc\uff0c\u841d\u535c\uff0c\u9ec4\u74dc\uff09\u3002\u771f\u8fd8\u522b\u5c0f\u770b\u8fd9\u5341\u4e94\u79cd\u666e\u901a\u852c\u83dc\uff0c\u5b83\u4eec\u4e00\u5171\u53ef\u4ee5\u505a\u51fa\u6bcf\u5929\u90fd\u4e0d\u540c\u76846435\u5929\u5927\u7ea6\u5341\u4e03\u5e74\u534a\u7684<\/span> <\/span><\/section>\n
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\u83dc\u8c31\u3002\u518d\u95ee\u4e00\u4e2a\u95ee\u9898\uff1a\u73b0\u5728\u8fd915\u79cd\u852c\u83dc\uff0c\u6bcf\u4e2a\u83dc\u8c31\u4f7f\u7528k\u22647\u79cd\u852c\u83dc\uff0c\u4e14\u4efb\u4f55\u4e24\u4e2a\u4e0d\u540c\u83dc\u8c31\u81f3\u5c11\u4f7f\u7528\u4e00\u79cd\u76f8\u540c\u852c\u83dc\uff0c\u6211\u4eec\u53ef\u4ee5\u6700\u591a\u505a\u51fa\u591a\u5c11\u4e2a\u8fd9\u6837\u7684\u83dc\u8c31\u5462\uff1f<\/span><\/section>\n

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\u8d85\u56fe\u548c\u793e\u4ea4\u7f51\u7edc<\/strong><\/span><\/section>\n
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 \u8d1d\u5c14\u70ed<\/span><\/section>\n
Claude Jacques Roger Berger\u5728\u5df4\u9ece\u5927\u5b66\u5b66\u4e60\u6570\u5b66\uff0c\u5e76\u5728\u83b7\u5f97\u7b2c\u4e00\u5b66\u4f4d\u540e\uff0c\u7ee7\u7eed\u5728Andr\u00e9  Lichnerowicz\u7684\u6307\u5bfc\u4e0b\u7ee7\u7eed\u653b\u8bfb\u535a\u58eb\u5b66\u4f4d\u3002\u4ed6\u4e8e1950\u5e74\u5f00\u59cb\u53d1\u8868\u6570\u5b66\u8bba\u6587\u3002\u540c\u5e74\uff0c\u4ed6\u53d1\u8868\u4e86\u4e24\u7bc7\u8bba\u6587\u3002\u7136\u540e\uff0c\u4ed6\u5c06\u8bba\u6587\u4e2d\u7684\u7b26\u53f7\u6f14\u7b97\u5e94\u7528\u4e8e\u7ec4\u5408\u5206\u6790\uff0c\u4f2f\u52aa\u5229\u6570\uff0c\u5dee\u5206\u65b9\u7a0b\uff0c\u5fae\u5206\u65b9\u7a0b\u548c\u53ef\u52a0\u6027\u56e0\u5b50\u3002\u57281951\u5e74\uff0c\u4ed6\u53c8\u53d1\u8868\u4e86\u4e24\u7bc7\u7b80\u77ed\u7684\u8bba\u6587\uff0c\u5373\u201c\u53d8\u6362\u7684\u53cd\u9762\u201d\u548c\u201c\u4ea4\u66ff\u7684\u53cd\u9762\u201d\uff0c\u5e76\u5ba3\u5e03\u4e86\u5404\u79cd\u7ed3\u679c\uff0c\u8fd9\u4e9b\u7ed3\u679c\u5c06\u5728\u5176\u8bba\u6587\u4e2d\u8fdb\u884c\u5168\u9762\u8ba8\u8bba\u3002\u4ed6\u4e8e1953\u5e74\u83b7\u5f97\u535a\u58eb\u5b66\u4f4d\uff0c\u5728\u535a\u58eb\u8bba\u6587\u4e2d\uff0c\u4ed6\u7814\u7a76\u4e86\u53ef\u4ee5\u83b7\u53d6\u5b8c\u7f8e\u4fe1\u606f\u7684\u6e38\u620f\uff0c\u5728\u8fd9\u4e9b\u4fe1\u606f\u4e2d\uff0c\u6bcf\u4e00\u6b65\u90fd\u53ef\u80fd\u6709\u65e0\u6570\u7684\u9009\u62e9\u3002\u6e38\u620f\u4e0d\u4e00\u5b9a\u662f\u6709\u9650\u7684\uff0c\u53ef\u4ee5\u65e0\u9650\u671f\u5ef6\u7eed\u3002\u8d1d\u5c14\u70ed\u901a\u8fc7\u8be6\u5c3d\u7684\u5206\u6790\u68c0\u67e5\u4e86\u6b64\u7c7b\u6e38\u620f\u7684\u5c5e\u6027\u3002<\/span><\/section>\n
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1952\u5e74\uff0c\u5728\u83b7\u5f97\u535a\u58eb\u5b66\u4f4d\u4e4b\u524d\uff0c\u8d1d\u5c14\u70ed\u88ab\u4efb\u547d\u4e3a\u56fd\u5bb6\u79d1\u5b66\u7814\u7a76\u6240\u7684\u7814\u7a76\u52a9\u7406\u30021957\u5e74\uff0c\u4ed6\u5728\u7f8e\u56fd\u666e\u6797\u65af\u987f\u5927\u5b66\u4efb\u5ba2\u5ea7\u6559\u6388\u3002\u53c2\u52a0\u4e86\u4e0e\u6d77\u519b\u7814\u7a76\u529e\u516c\u5ba4\u7b7e\u8ba2\u7684\u7ecf\u6d4e\u7814\u7a76\u9879\u76ee\u3002\u5728\u666e\u6797\u65af\u987f\u5927\u5b66\u671f\u95f4\uff0c\u8bba\u6587\u53d1\u8868\u5728\u7f8e\u56fd\u56fd\u5bb6\u79d1\u5b66\u9662\u9662\u520a\u4e0a\u3002\u8fd9\u662f\u4ed6\u5173\u4e8e\u56fe\u8bba\u7684\u65e9\u671f\u8bba\u6587\u4e4b\u4e00\uff0c\u4ed6\u8f83\u65e9\u7684\u5de5\u4f5c\u662f\u5173\u4e8e\u535a\u5f08\u8bba\u548c\u7ec4\u5408\u8bba\u7684\u3002\u4ed6\u5f53\u65f6\u6b63\u5728\u5199\u4ed6\u7684\u8457\u4f5c\u300aTh\u00e9oriedes graphes et ses applicationss \u300b\uff0c\u521a\u521a\u51fa\u7248\u4e86\u4ed6\u7684\u300aTh\u00e9orieg\u00e9n\u00e9raledes jeux\u00e0n personnes games \u300b\u6e38\u620f\u7406\u8bba\u4e66\uff081957\u5e74\uff09\u3002\u8d1d\u5c14\u70ed\u4ece\u7f8e\u56fd\u56de\u5230\u6cd5\u56fd\u540e\uff0c\u5728\u56fd\u5bb6\u79d1\u7814\u4e2d\u5fc3\u62c5\u4efb\u7814\u7a76\u4e3b\u4efb\u3002\u540c\u6837\u57281957\u5e74\uff0c\u4ed6\u88ab\u4efb\u547d\u4e3a\u5df4\u9ece\u5927\u5b66\u7edf\u8ba1\u7814\u7a76\u6240\u7684\u6559\u6388\u3002\u300aTh\u00e9oriedes graphes et ses applicationss \u300b\u4e8e1958\u5e74\u51fa\u7248\uff0c\u5e76\u4e8e\u6b21\u5e74\u51fa\u7248\u4e86\u4ed6\u7684\u7b2c\u4e09\u672c\u4e66\u300aEspaces topologiques,fuctions multivoques fon\u300b\u3002\u5bf9\u4e8e30\u5e74\u4ee3\u521d\u7684\u6570\u5b66\u5bb6\u6765\u8bf4\uff0c\u5728\u51e0\u5e74\u5185\u51fa\u7248\u4e09\u672c\u4e3b\u8981\u8457\u4f5c\u662f\u4e00\u9879\u771f\u6b63\u7684\u6770\u51fa\u6210\u5c31\u3002<\/span><\/section>\n
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