{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:33Z","timestamp":1753893813687,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A signed graph is a graph whose edges are given $\\pm 1$ weights. In such a graph, the sign of a cycle is the product of the signs of its edges. A signed graph is called balanced if its adjacency matrix is similar to the adjacency matrix of an unsigned graph via conjugation by a diagonal $\\pm 1$ matrix. For a signed graph $\\Sigma$ on $n$ vertices, its exterior $k$th power, where $k=1,\\ldots,n-1$, is a graph $\\bigwedge^{k} \\Sigma$ whose adjacency matrix is given by\\[ A(\\mbox{$\\bigwedge^{k} \\Sigma$}) = P_{\\wedge}^{\\dagger} A(\\Sigma^{\\Box k}) P_{\\wedge}, \\]where $P_{\\wedge}$ is the projector onto the anti-symmetric subspace of the $k$-fold tensor product space $(\\mathbb{C}^{n})^{\\otimes k}$ and $\\Sigma^{\\Box k}$ is the $k$-fold Cartesian product of $\\Sigma$ with itself. The exterior power creates a signed graph from any graph, even unsigned. We prove sufficient and necessary conditions so that $\\bigwedge^{k} \\Sigma$ is balanced. For $k=1,\\ldots,n-2$, the condition is that either $\\Sigma$ is a signed path or $\\Sigma$ is a signed cycle that is balanced for odd $k$ or is unbalanced for even $k$; for $k=n-1$, the condition is that each even cycle in $\\Sigma$ is positive and each odd cycle in $\\Sigma$ is negative.<\/jats:p>","DOI":"10.37236\/3033","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:32:18Z","timestamp":1578706338000},"source":"Crossref","is-referenced-by-count":2,"title":["Which Exterior Powers are Balanced?"],"prefix":"10.37236","volume":"20","author":[{"given":"Devlin","family":"Mallory","sequence":"first","affiliation":[]},{"given":"Abigail","family":"Raz","sequence":"additional","affiliation":[]},{"given":"Christino","family":"Tamon","sequence":"additional","affiliation":[]},{"given":"Thomas","family":"Zaslavsky","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,5,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p43\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p43\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:19:13Z","timestamp":1579259953000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i2p43"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,31]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2013,4,9]]}},"URL":"https:\/\/doi.org\/10.37236\/3033","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,5,31]]},"article-number":"P43"}}