{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T10:22:57Z","timestamp":1775643777786,"version":"3.50.1"},"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>For any $q \\geq 2$,  let $\\Sigma_{q}=\\{0,\\ldots,q\\!-\\!1\\}$, and fix a string $A$ over $\\Sigma_{q}$. The $A$-free strings of length $n$ are the strings in $\\Sigma_{q}^n$ which do not contain $A$ as a contiguous substring. In this paper, we investigate the possibility of listing the $A$-free strings of length $n$ so that successive strings differ in only one position, and by $\\pm 1$ in that position. Such a listing is a Gray code for  the $A$-free strings of length $n$. We identify those $q$ and $A$ such that, for infinitely many $n \\geq 0$, a Gray code  for the $A$-free strings of length $n$ is prohibited by a parity problem. Our parity argument uses techniques similar to those of Guibas and Odlyzko (Journal of Combinatorial Theory A  30 (1981) pp. 183\u2013208)  who enumerated the $A$-free strings of length $n$. When $q$ is even, we also give the complementary positive result: for those $A$ for which  an infinite number of parity problems do not exist,  we construct a Gray code for the $A$-free strings of length $n$ for all $n \\geq 0$.<\/jats:p>","DOI":"10.37236\/1241","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:50:21Z","timestamp":1578707421000},"source":"Crossref","is-referenced-by-count":7,"title":["Gray Codes for A-Free Strings"],"prefix":"10.37236","volume":"3","author":[{"given":"Matthew B.","family":"Squire","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1996,2,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i1r17\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i1r17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T06:17:48Z","timestamp":1579328268000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v3i1r17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,2,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1996,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1241","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,2,14]]},"article-number":"R17"}}