{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:30Z","timestamp":1753893810340,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Triangular fully packed loop configurations (TFPLs) came up in the study of fully packed loop configurations on a square (FPLs) corresponding to link patterns with a large number of nested arches. To a TFPL is assigned a triple $(u,v;w)$ of $01$-words encoding its boundary conditions which must necessarily satisfy that $d(u)+d(v)\\leq d(w)$, where $d(u)$ denotes the number of inversions in $u$. Wieland gyration, on the other hand, was invented to show the rotational invariance of the numbers of FPLs having given link patterns. Later, Wieland drift \u2014 a map on TFPLs that is based on Wieland gyration \u2014 was defined. The main contribution of this article will be a linear expression for the number of TFPLs with boundary $(u,v;w)$ where $d(w)-d(u)-d(v)=2$ in terms of numbers of stable TFPLs, that is, TFPLs invariant under Wieland drift.\u00a0This linear expression generalises already existing enumeration results for TFPLs with boundary $(u,v;w)$ where $d(w)-d(u)-d(v)=0,1$.<\/jats:p>","DOI":"10.37236\/5536","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:03:51Z","timestamp":1578686631000},"source":"Crossref","is-referenced-by-count":0,"title":["Triangular Fully Packed Loop Configurations of Excess 2"],"prefix":"10.37236","volume":"23","author":[{"given":"Sabine","family":"Beil","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,10,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:11:12Z","timestamp":1579237872000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i4p14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,28]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2016,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/5536","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,10,28]]},"article-number":"P4.14"}}