{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T01:18:43Z","timestamp":1649035123130},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"Given a finite set $E$, a subset $D\\subseteq E$ (viewed as a function $E\\to \\mathbb F_2$) is orthogonal to a given subspace $\\mathcal F$ of the $\\mathbb F_2$-vector space of functions $E\\to \\mathbb F_2$ as soon as $D$ is orthogonal to every $\\subseteq$-minimal element of $\\mathcal F$. This fails in general when $E$ is infinite.However, we prove the above statement for the six subspaces $\\mathcal F$ of the edge space of any $3$-connected locally finite graph that are relevant to its homology: the topological, algebraic, and finite cycle and cut spaces. This solves a problem of Diestel (2010, arXiv:0912.4213).<\/jats:p>","DOI":"10.37236\/3844","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:55:56Z","timestamp":1578704156000},"source":"Crossref","is-referenced-by-count":0,"title":["Orthogonality and Minimality in the Homology of Locally Finite Graphs"],"prefix":"10.37236","volume":"21","author":[{"given":"Reinhard","family":"Diestel","sequence":"first","affiliation":[]},{"given":"Julian","family":"Pott","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2014,9,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i3p36\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i3p36\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:49:04Z","timestamp":1579258144000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i3p36"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9,11]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2014,7,3]]}},"URL":"https:\/\/doi.org\/10.37236\/3844","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9,11]]}}}