{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:26Z","timestamp":1753893806074,"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>Let $\\mathcal{P}_n$ be the set of all binary paths (i.e., lattice paths with upsteps $u = (1,1)$ and downsteps $d = (1,-1)$) of length $n$ endowed with the pointwise partial ordering (i.e., $P \\le Q$ iff the lattice path $P$ lies weakly below $Q$) and let $G_n$ be its Hasse graph. For each path $P \\in \\mathcal{P}_n$, we denote by $I(P)$ the interval which contains the elements of $\\mathcal{P}_n$ less than or equal to $P$, excluding the first two elements of $\\mathcal{P}_n$, and by $G(P)$ the subgraph of $G_n$ induced by $I(P)$. In this paper, it is shown that $G(P)$ is Hamiltonian iff $P$ contains at least two peaks and $I(P)$ has equal number of elements with even and odd rank. The last condition is always true for paths ending with an upstep, whereas, for paths ending with a downstep, a simple characterization is given, based on the structure of the path.<\/jats:p>","DOI":"10.37236\/12144","type":"journal-article","created":{"date-parts":[[2024,2,9]],"date-time":"2024-02-09T15:45:27Z","timestamp":1707493527000},"source":"Crossref","is-referenced-by-count":0,"title":["Hamiltonian Intervals in the Lattice of Binary Paths"],"prefix":"10.37236","volume":"31","author":[{"given":"I.","family":"Tasoulas","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K.","family":"Manes","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Sapounakis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2024,2,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i1p39\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i1p39\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,9]],"date-time":"2024-02-09T15:45:27Z","timestamp":1707493527000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i1p39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/12144","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2024,2,9]]},"article-number":"P1.39"}}