{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T16:12:48Z","timestamp":1765469568500,"version":"3.48.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We show that the minimal number of skewed hyperplanes that cover the hypercube $\\{0,1\\}^{n}$ is at least $\\frac{n}{2}+1$, and there are infinitely many $n$'s when the hypercube can be covered with $n-\\log_{2}(n)+1$ skewed hyperplanes. The minimal covering problems are closely related to the uncertainty principle on the hypercube, where we also obtain an interpolation formula for multilinear polynomials on $\\mathbb{R}^{n}$ of degree less than $\\lfloor n\/m \\rfloor$ by showing that its coefficients corresponding to the largest monomials can be represented as a linear combination of values of the polynomial over the points $\\{0,1\\}^{n}$ whose Hamming weights are divisible by $m$.<\/jats:p>","DOI":"10.37236\/12756","type":"journal-article","created":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T16:08:12Z","timestamp":1765469292000},"source":"Crossref","is-referenced-by-count":0,"title":["Covering the Hypercube, the Uncertainty Principle, and an Interpolation Formula"],"prefix":"10.37236","volume":"32","author":[{"given":"Paata","family":"Ivanisvili","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ohad","family":"Klein","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roman","family":"Vershynin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2025,12,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i4p69\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i4p69\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T16:08:12Z","timestamp":1765469292000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i4p69"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,12]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,10,3]]}},"URL":"https:\/\/doi.org\/10.37236\/12756","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,12]]},"article-number":"P4.69"}}