{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:48Z","timestamp":1753893828641,"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 characterize symmetric transversal designs ${\\rm STD}_{\\lambda}[k,u]$'s which have a semiregular automorphism group $G$ on both points and blocks containing an elation group of order $u$ using the group ring ${\\bf Z}[G]$. Let $n_\\lambda$ be the number of nonisomorphic ${\\rm STD}_{\\lambda}[3\\lambda,3]$'s. It is known that $n_1=1,\\ n_2=1,\\ n_3=4, n_4=1$, and $n_5=0$.  We classify ${\\rm STD}_6[18,3]$'s and ${\\rm STD}_7[21,3]$'s which have a semiregular noncyclic automorphism group of order 9 on both points and blocks containing an elation of order 3 using this characterization.  The former case yields exactly twenty nonisomorphic ${\\rm STD}_6[18,3]$'s and the latter case yields exactly three nonisomorphic ${\\rm STD}_7[21,3]$'s. These yield $n_6\\geq20$ and $n_7\\geq 5$, because B. Brock and A. Murray constructed two other ${\\rm STD}_7[21,3]$'s in 1991.  We used a computer for our research.<\/jats:p>","DOI":"10.37236\/237","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:23:25Z","timestamp":1578716605000},"source":"Crossref","is-referenced-by-count":1,"title":["On ${\\rm STD}_6[18,3]$'s and ${\\rm STD}_7[21,3]$'s Admitting a Semiregular Automorphism Group of Order 9"],"prefix":"10.37236","volume":"16","author":[{"given":"Kenzi","family":"Akiyama","sequence":"first","affiliation":[]},{"given":"Masayuki","family":"Ogawa","sequence":"additional","affiliation":[]},{"given":"Chihiro","family":"Suetake","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,12,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r148\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r148\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:03:20Z","timestamp":1579305800000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r148"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12,8]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/237","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,12,8]]},"article-number":"R148"}}