{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:04Z","timestamp":1753893844596,"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>We examine sequences containing $p$ \"$-t$\"s and $pt+r$ \"$+1$\"s, where $p$, $t$, and $r$ are integers satisfying $p\\ge0$, $t\\ge 1$ and $pt+r\\ge0$. We develop a rotation method to enumerate the number of sequences meeting additional requirements related to their partial sums.  We also define downcrossings about $\\ell$ and their downcrossing numbers, and obtain formulas for the number of sequences for which the sum of the downcrossing numbers equals $k$, for $\\ell \\le r+1$.  We finish with an investigation of the first downcrossing number about $\\ell$, for any $\\ell$. <\/jats:p>","DOI":"10.37236\/432","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:59:09Z","timestamp":1578697149000},"source":"Crossref","is-referenced-by-count":0,"title":["The Enumeration of Sequences with Restrictions on their Partial Sums"],"prefix":"10.37236","volume":"17","author":[{"given":"Stephen","family":"Suen","sequence":"first","affiliation":[]},{"given":"Kevin P.","family":"Wagner","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,11,26]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r160\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r160\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:21:41Z","timestamp":1579285301000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r160"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,11,26]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/432","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,11,26]]},"article-number":"R160"}}