{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:35Z","timestamp":1753893815190,"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>In this article, we study the enumeration by length of several walk models on the square lattice. We obtain bijections between walks in the upper half-plane returning to the $x$-axis and walks in the quarter plane. A recent work by Bostan, Chyzak, and Mahboubi has given a bijection for models using small north, west, and south-east steps. We adapt and generalize it to a bijection between half-plane walks using those three steps in two colours and a quarter-plane model over the symmetrized step set consisting of north, north-west, west, south, south-east, and east. We then generalize our bijections to certain models with large steps: for given $p\\geq1$, a bijection is given between the half-plane and quarter-plane models obtained by keeping the small south-east step and replacing the two steps north and west of length 1 by the $p+1$ steps of length $p$ in directions between north and west. This model is close to, but distinct from, the model of generalized tandem walks studied by Bousquet-M\u00e9lou, Fusy, and Raschel.<\/jats:p>","DOI":"10.37236\/8261","type":"journal-article","created":{"date-parts":[[2020,4,3]],"date-time":"2020-04-03T03:56:00Z","timestamp":1585886160000},"source":"Crossref","is-referenced-by-count":1,"title":["Bijections between \u0141ukasiewicz Walks and Generalized Tandem Walks"],"prefix":"10.37236","volume":"27","author":[{"given":"Fr\u00e9d\u00e9ric","family":"Chyzak","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karen","family":"Yeats","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,4,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p3\/8060","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p3\/8060","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,3]],"date-time":"2020-04-03T03:56:11Z","timestamp":1585886171000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i2p3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,3]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8261","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,4,3]]},"article-number":"P2.3"}}