{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:41Z","timestamp":1753893821998,"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>A $k$-factorization of $K_v$ of type $(r, s)$ consists of $k$-factors each of which is the disjoint union of $r$ copies of $K_{k+1}$ and $s$ copies of $K_{k,k}$. By means of what we call the patterned $k$-factorization $F_k(D)$ over an arbitrary group $D$ of order $2s + 1$, it is shown that a $k$-factorization of type $(1, s)$ exists for any $k\\ge2$ and for any $s\\ge1$ with $D$ being an automorphism group acting sharply transitively on the factor-set. The general method to construct a $k$-factorization $F$ of type $(1, s)$ over an arbitrary 1-factorization $S$ of $K_{2s+2}$ ($F$ is said to be based on $S$) is used to prove that the number of pairwise non-isomorphic $k$-factorizations of this type goes to infinity with $s$. In this paper, we show that the full automorphism group of $F$ is known as soon as we know the one of $S$. In particular, the full automorphism group of $F_k(D)$ is determined for any $k\\ge2$, generalizing a result given by P. J. Cameron for patterned 1-factorizations [J London Math Soc 11 (1975), 189-201]. Finally, it is shown that $F_k(D)$ has exactly $(k!)2s+1(2s+1)|Aut(D)|$ automorphisms whenever $D$ is abelian.<\/jats:p>","DOI":"10.37236\/2149","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:00:05Z","timestamp":1578711605000},"source":"Crossref","is-referenced-by-count":1,"title":["On a Class of Highly Symmetric k-Factorizations"],"prefix":"10.37236","volume":"20","author":[{"given":"Tommaso","family":"Traetta","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,2,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p24\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:27:24Z","timestamp":1579260444000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2149","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,2,5]]},"article-number":"P24"}}