{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T15:00:46Z","timestamp":1779289246807,"version":"3.51.4"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper, we start by considering generating function identities for linked partition ideals in the setting of basic graph theory. Then our attention is turned to $q$-difference systems, which eventually lead to a factorization problem of a special type of column functional vectors involving $q$-multi-summations. Using a recurrence relation satisfied by certain $q$-multi-summations, we are able to provide non-computer-assisted proofs of some Andrews--Gordon type generating function identities. These proofs also have an interesting connection with binary trees. Further, we give illustrations of constructing a linked partition ideal, or more loosely, a set of integer partitions whose generating function corresponds to a given set of special $q$-multi-summations.<\/jats:p>","DOI":"10.37236\/9446","type":"journal-article","created":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:47:32Z","timestamp":1599187652000},"source":"Crossref","is-referenced-by-count":6,"title":["Linked Partition Ideals, Directed Graphs and $q$-Multi-Summations"],"prefix":"10.37236","volume":"27","author":[{"given":"Shane","family":"Chern","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,8,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p33\/8151","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p33\/8151","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:47:32Z","timestamp":1599187652000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,21]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,7,9]]}},"URL":"https:\/\/doi.org\/10.37236\/9446","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,21]]},"article-number":"P3.33"}}