{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:21Z","timestamp":1753893801088,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The Sandwich Theorems proved in this paper give a new method to show that the partition function $a(n)$ of a partition identity $$ {\\bf A}(x) \\ :=\\ \\sum_{n=0}^\\infty a(n)x^n\\ =\\  \\prod_{n=1}^\\infty (1-x^n)^{-p(n)} $$ satisfies the condition RT$_1$ $$ \\lim_{n\\rightarrow \\infty}{a(n-1)\\over a(n)} \\ =\\ 1\\,. $$ This leads to numerous examples of naturally occuring  classes of relational structures  whose finite members enjoy a logical 0\u20131 law. <\/jats:p>","DOI":"10.37236\/1802","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:20:53Z","timestamp":1578720053000},"source":"Crossref","is-referenced-by-count":1,"title":["Partition Identities I: Sandwich Theorems and Logical 0&amp;ndash;1 Laws"],"prefix":"10.37236","volume":"11","author":[{"given":"Jason P.","family":"Bell","sequence":"first","affiliation":[]},{"given":"Stanley N.","family":"Burris","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,7,26]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r49\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r49\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:01:51Z","timestamp":1579323711000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,7,26]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1802","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2004,7,26]]},"article-number":"R49"}}