{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T07:22:20Z","timestamp":1791444140168,"version":"4.3.3"},"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>In this work we consider weighted lattice paths in the quarter plane ${\\Bbb N}_0\\times{\\Bbb N}_0$.  The steps are given by $(m,n)\\to(m-1,n)$, $(m,n)\\to(m,n-1)$ and are weighted as follows: $(m,n)\\to(m-1,n)$ by $m\/(m+n)$ and step $(m,n)\\to(m,n-1)$ by $n\/(m+n)$. The considered lattice paths are absorbed at lines $y=x\/t -s\/t$ with $t\\in{\\Bbb N}$ and $s\\in{\\Bbb N}_0$.  We provide explicit formul\u00e6 for the sum of the weights of paths, starting at $(m,n)$, which are absorbed at a certain height $k$ at lines $y=x\/t -s\/t$ with $t\\in{\\Bbb N}$ and $s\\in{\\Bbb N}_0$, using a generating functions approach. Furthermore these weighted lattice paths can be interpreted as probability distributions arising in the context of P\u00f3lya-Eggenberger urn models, more precisely, the lattice paths are sample paths of the well known sampling without replacement urn. We provide limiting distribution results for the underlying random variable, obtaining a total of five phase changes.<\/jats:p>","DOI":"10.37236\/156","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:31:17Z","timestamp":1578717077000},"source":"Crossref","is-referenced-by-count":2,"title":["Lattice Paths, Sampling Without Replacement, and Limiting Distributions"],"prefix":"10.37236","volume":"16","author":[{"given":"M.","family":"Kuba","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Panholzer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"H.","family":"Prodinger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2009,5,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r67\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r67\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:53:19Z","timestamp":1579315999000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r67"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/156","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,5,29]]},"article-number":"R67"}}