{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:42:53Z","timestamp":1753893773592,"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  $\\lambda-Triple\\ System(v)$, or a $\\lambda $\u2013$TS(V,\\cal{B})$, is a pair (V, $\\cal{B}$) where V is a set and $\\cal{B}$ is a subset of the 3-subsets of V so that every pair is in exactly $\\lambda$ elements of $\\cal{B}$. A $regular\\ configuration$ on p points with regularity $\\rho$ on $l$ blocks   is a pair (P,${\\cal L}$) where $\\cal{L}$ is a collection of 3-subsets of a (usually small) set P so that every p in P is in exactly $\\rho$ elements of ${\\cal L}$, and $|{\\cal L}|=l$. The Pasch configuration $(\\{0,1,2,3,4,5\\},\\{ 012,035,245,134\\})$ has p=6, $l$=4, and $\\rho$=2. A $\\lambda$\u2013$TS(V,\\cal{B})$, is resolvable into a regular configuration ${\\Bbb C}$=(P,${\\cal L}$), or ${\\Bbb C}$\u2013resolvable, if  ${\\cal B}$ can be partitioned into sets $\\Pi_{i}$ so that for each i, (V,$\\Pi_{i}$) is isomorphic to a set of vertex disjoint copies of (P,${\\cal L}$). If the configuration is a single block on three points this corresponds to ordinary resolvability of a Triple System. In this paper we examine all regular configurations ${\\Bbb C}$ on 6 or fewer blocks and construct ${\\Bbb C}$\u2013resolvable $\\lambda$\u2013Triple Systems of order v for many values of v and $\\lambda$. These conditions are also sufficient for each ${\\Bbb C}$ having 4 blocks or fewer. For example for the Pasch configuration $\\lambda \\equiv 0 \\pmod{4}$ and $v \\equiv 0 \\pmod{6}$  are necessary and sufficient.<\/jats:p>","DOI":"10.37236\/1480","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:05:53Z","timestamp":1578690353000},"source":"Crossref","is-referenced-by-count":0,"title":["Resolving Triple Systems into Regular Configurations"],"prefix":"10.37236","volume":"7","author":[{"given":"E.","family":"Mendelsohn","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G.","family":"Quattrocchi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[1999,11,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r2\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r2\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:31:51Z","timestamp":1579307511000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v7i1r2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,11,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2000,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1480","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1999,11,22]]},"article-number":"R2"}}