{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:49Z","timestamp":1753893829106,"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>Consider the unit triangular lattice in the plane with origin\u00a0$O$, drawn so that one of the sets of lattice lines is vertical. Let $l$ and\u00a0$l'$ denote respectively the vertical and horizontal lines that\u00a0intersect $O$. Suppose the plane contains a pair of triangular holes of side\u00a0length two,\u00a0distributed symmetrically with respect to $l$ and $l'$ and oriented so that\u00a0both holes point toward the origin. In the following article rhombus tilings of three different\u00a0regions of the plane are considered, namely: tilings of the entire plane;\u00a0tilings of the half plane that lies to the left of $l$ (where $l$ is considered\u00a0a free boundary, so unit rhombi are allowed to protrude halfway across it);\u00a0and tilings of the half plane that lies just below the fixed boundary $l'$.\u00a0Asymptotic expressions for the interactions of the triangular holes in these\u00a0three different regions are obtained thus providing further evidence for Ciucu's\u00a0ongoing program that seeks to draw parallels between gaps in dimer systems on\u00a0the hexagonal lattice and certain electrostatic phenomena.<\/jats:p>","DOI":"10.37236\/6353","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:55:31Z","timestamp":1578671731000},"source":"Crossref","is-referenced-by-count":1,"title":["Three Interactions of Holes in Two Dimensional Dimer Systems"],"prefix":"10.37236","volume":"24","author":[{"given":"Tomack","family":"Gilmore","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,5,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i2p17\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i2p17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:57:18Z","timestamp":1579237038000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i2p17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,5]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/6353","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,5,5]]},"article-number":"P2.17"}}