{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:38Z","timestamp":1753893818765,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Using potential theoretic techniques, we show how it is possible to determine the dominant asymptotics for the number of walks of\u00a0length $n$, restricted to the positive quadrant and taking unit steps in a balanced set $\\Gamma$. The approach is illustrated through an example of inhomogeneous space walk. This walk takes its steps in $\\{ \\leftarrow, \\uparrow, \\rightarrow, \\downarrow \\}$ or $\\{ \\swarrow, \\leftarrow, \\nwarrow, \\uparrow,\\nearrow, \\rightarrow, \\searrow, \\downarrow \\}$, depending on the parity of the coordinates of its positions.\u00a0The exponential growth of our model is $(4\\phi)^n$, where $\\phi= \\frac{1+\\sqrt 5}{2}$denotes the Golden ratio, while the subexponential growth is like $1\/n$.As an application of our approach we prove the non-D-finiteness in two dimensions of the length generating functions corresponding to nonsingular small step sets with an infinite group and zero-drift. <\/jats:p>","DOI":"10.37236\/5877","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T16:07:35Z","timestamp":1578672455000},"source":"Crossref","is-referenced-by-count":2,"title":["Combinatorics Meets Potential Theory"],"prefix":"10.37236","volume":"23","author":[{"given":"Philippe","family":"D'Arco","sequence":"first","affiliation":[]},{"given":"Valentina","family":"Lacivita","sequence":"additional","affiliation":[]},{"given":"Sami","family":"Mustapha","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,5,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p28\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p28\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T00:28:21Z","timestamp":1579220901000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i2p28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,13]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/5877","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,5,13]]},"article-number":"P2.28"}}