{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T20:10:17Z","timestamp":1774555817130,"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>Given a set $S$, an integer $k$ and a permutation group $G$ acting on $S$, we provide a novel algorithm for computing ${S \\choose k}_{G}$, which is the set of all $k$-subsets of $S$ up to symmetries in $G$. Then we apply our algorithm to compute $(d,g)$-cages which are $d$-regular graphs of girth $g$ and minimum order $n=n(d,g)$. Our algorithm allowed us to reproduce most of the computational results on cages and to improve six lower bounds for the order of cages, namely: $n(3,14)\\geq 262$, $n(3,15)\\geq 388$, $n(3,17)\\geq 770$, $n(4,9)\\geq 165$, $n(5,7)\\geq 110$ and $n(8,5) \\geq 69$.<\/jats:p>","DOI":"10.37236\/14471","type":"journal-article","created":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T19:48:24Z","timestamp":1774554504000},"source":"Crossref","is-referenced-by-count":0,"title":["On Cages and Choosing with Symmetries"],"prefix":"10.37236","volume":"33","author":[{"given":"C. M.","family":"De la Cruz","sequence":"first","affiliation":[]},{"given":"M. A.","family":"Piza\u00f1a","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2026,3,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p54\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p54\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T19:48:24Z","timestamp":1774554504000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i1p54"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,27]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/14471","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,27]]},"article-number":"P1.54"}}