{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T11:05:49Z","timestamp":1780743949887,"version":"3.54.1"},"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>Let $Q_d$ be the $d$-dimensional Hamming cube and $N=|V(Q_d)|=2^d$. An independent set $I$ in $Q_d$ is called balanced if $I$ contains the same number of even and odd vertices. We show that the logarithm of the number of balanced independent sets in $Q_d$ is\r\n\\[(1-\\Theta(1\/\\sqrt d))N\/2.\\]\r\nThe key ingredient of the proof is an improved version of \"Sapozhenko's graph container lemma\".<\/jats:p>","DOI":"10.37236\/10471","type":"journal-article","created":{"date-parts":[[2022,5,19]],"date-time":"2022-05-19T07:46:04Z","timestamp":1652946364000},"source":"Crossref","is-referenced-by-count":7,"title":["Note on the Number of Balanced Independent Sets in the Hamming Cube"],"prefix":"10.37236","volume":"29","author":[{"given":"Jinyoung","family":"Park","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2022,5,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i2p34\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i2p34\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,19]],"date-time":"2022-05-19T07:46:04Z","timestamp":1652946364000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i2p34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,20]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,4,8]]}},"URL":"https:\/\/doi.org\/10.37236\/10471","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,20]]},"article-number":"P2.34"}}