{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:12Z","timestamp":1753893852065,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The sequence $(x_n)_{n\\in\\mathbb N} = (2,5,15,51,187,\\ldots)$ given by the rule $x_n=(2^n+1)(2^{n-1}+1)\/3$ appears in several seemingly unrelated areas of mathematics.\u00a0For example, $x_n$ is the density of a language of words of length $n$ with four different letters.\u00a0It is also the cardinality of the quotient of $(\\mathbb Z_2\\times \\mathbb Z_2)^n$ under the left action of the special linear group $\\mathrm{SL}(2,\\mathbb Z)$.\u00a0In this paper we show how these two interpretations of $x_n$ are related to each other.\u00a0More generally, for prime numbers $p$ we show a correspondence between a quotient of $(\\mathbb Z_p\\times\\mathbb Z_p)^n$ and a language with $p^2$ letters and words of length $n$.<\/jats:p>","DOI":"10.37236\/4668","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T18:26:05Z","timestamp":1578680765000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Density of Certain Languages with $p^2$ Letters"],"prefix":"10.37236","volume":"22","author":[{"given":"Carlos","family":"Segovia","sequence":"first","affiliation":[]},{"given":"Monika","family":"Winklmeier","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,7,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i3p16\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i3p16\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:14:02Z","timestamp":1579238042000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i3p16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,31]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2015,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/4668","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,7,31]]},"article-number":"P3.16"}}