{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:58Z","timestamp":1753893838788,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>This work focuses on higgledy-piggledy sets of $k$-subspaces in $\\text{PG}(N,q)$, i.e. sets of projective subspaces that are 'well-spread-out'. More precisely, the set of intersection points of these $k$-subspaces with any $(N-k)$ subspace $\\kappa$ of $\\text{PG}(N,q)$ spans $\\kappa$ itself.\r\nWe highlight three methods to construct small higgledy-piggledy sets of $k$-subspaces and discuss, for $k\\in\\{1,N-2\\}$, 'optimal' sets that cover the smallest possible number of points.\r\nFurthermore, we investigate small non-trivial higgledy-piggledy sets in $\\text{PG}(N,q)$, $N\\leqslant5$. Our main result is the existence of six lines of $\\text{PG}(4,q)$ in higgledy-piggledy arrangement, two of which intersect. Exploiting the construction methods mentioned above, we also show the existence of six planes of $\\text{PG}(4,q)$ in higgledy-piggledy arrangement, two of which maximally intersect, as well as the existence of two higgledy-piggledy sets in $\\text{PG}(5,q)$ consisting of eight planes and seven solids, respectively. Finally, we translate these geometrical results to a coding- and graph-theoretical context.<\/jats:p>","DOI":"10.37236\/10736","type":"journal-article","created":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T15:04:55Z","timestamp":1659107095000},"source":"Crossref","is-referenced-by-count":1,"title":["Higgledy-Piggledy Sets in Projective Spaces of Small Dimension"],"prefix":"10.37236","volume":"29","author":[{"given":"Lins","family":"Denaux","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2022,7,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i3p29\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i3p29\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T15:05:17Z","timestamp":1659107117000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i3p29"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,29]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/10736","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2022,7,29]]},"article-number":"P3.29"}}