{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T13:11:45Z","timestamp":1744117905492,"version":"3.37.3"},"reference-count":0,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2017,12]]},"abstract":"<jats:p> A dispersed Dyck path (DDP) of length [Formula: see text] is a lattice path on [Formula: see text] from [Formula: see text] to [Formula: see text] in which the following steps are allowed: \u201cup\u201d [Formula: see text]; \u201cdown\u201d [Formula: see text]; and \u201cright\u201d [Formula: see text]. An ascent in a DDP is an inclusion-wise maximal sequence of consecutive up steps. A 1-ascent is an ascent consisting of exactly 1 up step. <\/jats:p><jats:p> We give a closed formula for the total number of 1-ascents in all dispersed Dyck paths of length [Formula: see text], #A191386 in Sloane\u2019s OEIS. Previously, only implicit generating function relations and asymptotics were known. <\/jats:p>","DOI":"10.1142\/s179383091750077x","type":"journal-article","created":{"date-parts":[[2017,11,15]],"date-time":"2017-11-15T02:55:39Z","timestamp":1510714539000},"page":"1750077","source":"Crossref","is-referenced-by-count":1,"title":["Short note on the number of 1-ascents in dispersed Dyck paths"],"prefix":"10.1142","volume":"09","author":[{"given":"Kairi","family":"Kangro","sequence":"first","affiliation":[{"name":"Institute of Computer Science, University of Tartu, \u00dclikooli 17, 51014 Tartu, Estonia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2092-816X","authenticated-orcid":false,"given":"Mozhgan","family":"Pourmoradnasseri","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, University of Tartu, \u00dclikooli 17, 51014 Tartu, Estonia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dirk Oliver","family":"Theis","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, University of Tartu, \u00dclikooli 17, 51014 Tartu, Estonia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2017,12,13]]},"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S179383091750077X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T10:20:01Z","timestamp":1565173201000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S179383091750077X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12]]},"references-count":0,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2017,12,13]]},"published-print":{"date-parts":[[2017,12]]}},"alternative-id":["10.1142\/S179383091750077X"],"URL":"https:\/\/doi.org\/10.1142\/s179383091750077x","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2017,12]]}}}