{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:56Z","timestamp":1753893836988,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For integers $d$ and $k$ satisfying $0 \\le d \\le k$, a binary sequence is said to satisfy a one-dimensional $(d,k)$ run length constraint if there are never more than $k$ zeros in a row, and if between any two ones there are at least $d$ zeros. For $n\\geq 1$, the $n$-dimensional $(d,k)$-constrained capacity is defined as $$C^{n}_{d,k} = \\lim_{m_1,m_2,\\ldots,m_n\\rightarrow\\infty} {{\\log_2 N_{m_1,m_2,\\ldots ,m_n}^{(n; d,k)}} \\over {m_1 m_2\\cdots m_n}} $$ where $N_{m_1,m_2,\\ldots ,m_n}^{(n; d,k)}$ denotes the number of $m_1\\times m_2\\times\\cdots\\times m_n$ $n$-dimensional binary rectangular patterns that satisfy the one-dimensional $(d,k)$ run length constraint in the direction of every coordinate axis. It is proven for all $n\\ge 2$, $d\\ge1$, and $k&gt;d$ that $C^{n}_{d,k}=0$ if and only if $k=d+1$. Also, it is proven for every $d\\geq 0$ and $k\\geq d$ that $\\lim_{n\\rightarrow\\infty}C^{n}_{d,k}=0$ if and only if $k\\le 2d$.<\/jats:p>","DOI":"10.37236\/1465","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:00:16Z","timestamp":1578690016000},"source":"Crossref","is-referenced-by-count":13,"title":["Zero Capacity Region of Multidimensional Run Length Constraints"],"prefix":"10.37236","volume":"6","author":[{"given":"Hisashi","family":"Ito","sequence":"first","affiliation":[]},{"given":"Akiko","family":"Kato","sequence":"additional","affiliation":[]},{"given":"Zsigmond","family":"Nagy","sequence":"additional","affiliation":[]},{"given":"Kenneth","family":"Zeger","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1999,9,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r33\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:32:32Z","timestamp":1579307552000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v6i1r33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,9,1]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1999,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1465","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1999,9,1]]},"article-number":"R33"}}