{"title":"生成一些大的拟序格滤波器","authors":"Gábor Czédli","doi":"10.1007/s44146-024-00139-5","DOIUrl":null,"url":null,"abstract":"<div><p>For a poset <span>\\((P;\\le )\\)</span>, the quasiorders (AKA preorders) extending the poset order “<span>\\(\\le \\)</span>” form a complete lattice <i>F</i>, which is a filter in the lattice of all quasiorders of the set <i>P</i>. We prove that if the poset order “<span>\\(\\le \\)</span>” is small, then <i>F</i> can be generated by few elements.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"91 1-2","pages":"1 - 21"},"PeriodicalIF":0.6000,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generating some large filters of quasiorder lattices\",\"authors\":\"Gábor Czédli\",\"doi\":\"10.1007/s44146-024-00139-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For a poset <span>\\\\((P;\\\\le )\\\\)</span>, the quasiorders (AKA preorders) extending the poset order “<span>\\\\(\\\\le \\\\)</span>” form a complete lattice <i>F</i>, which is a filter in the lattice of all quasiorders of the set <i>P</i>. We prove that if the poset order “<span>\\\\(\\\\le \\\\)</span>” is small, then <i>F</i> can be generated by few elements.</p></div>\",\"PeriodicalId\":46939,\"journal\":{\"name\":\"ACTA SCIENTIARUM MATHEMATICARUM\",\"volume\":\"91 1-2\",\"pages\":\"1 - 21\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-05-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACTA SCIENTIARUM MATHEMATICARUM\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s44146-024-00139-5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACTA SCIENTIARUM MATHEMATICARUM","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s44146-024-00139-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Generating some large filters of quasiorder lattices
For a poset \((P;\le )\), the quasiorders (AKA preorders) extending the poset order “\(\le \)” form a complete lattice F, which is a filter in the lattice of all quasiorders of the set P. We prove that if the poset order “\(\le \)” is small, then F can be generated by few elements.