{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:01Z","timestamp":1753893841422,"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>We study compositions $c_1,\\dots,c_k$ of the integer $n$ in which adjacent parts may be constrained to satisfy some periodic inequalities, for example $$ c_{2i}&gt;c_{2i+1} &lt; c_{2i+2}   \\mbox{(alternating compositions).} $$ The types of inequalities considered are $ &lt; $, $\\le$, $&gt;$, $\\ge$ and $\\ne$. We show how to obtain generating functions from which various pieces of asymptotic information can be computed. There are asymptotically $Ar^{-n}$ compositions of $n$. In a random uniformly selected composition of $n$, the largest part and number of distinct parts are almost surely asymptotic to $\\log_{1\/r}(n)$. The length of the longest run is almost surely asymptotic to $C\\log_{1\/r}(n)$ where C is an easily determined rational number. Many other counts are asymptotically normally distributed. We present some numerical results for the various types of alternating compositions.<\/jats:p>","DOI":"10.37236\/417","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:59:54Z","timestamp":1578697194000},"source":"Crossref","is-referenced-by-count":1,"title":["Locally Restricted Compositions III. Adjacent-Part Periodic Inequalities"],"prefix":"10.37236","volume":"17","author":[{"given":"Edward A.","family":"Bender","sequence":"first","affiliation":[]},{"given":"E. Rodney","family":"Canfield","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,10,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r145\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r145\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:22:24Z","timestamp":1579285344000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r145"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,10,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/417","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,10,29]]},"article-number":"R145"}}