{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:26Z","timestamp":1753893866396,"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>We exhibit a connection between two statistics on set partitions, the intertwining number and the depth-index. In particular, results link the intertwining number to the algebraic geometry of Borel orbits. Furthermore, by studying the generating polynomials of our statistics, we determine the $q=-1$ specialization of a $q$-analogue of the Bell numbers. Finally, by using Renner's $H$-polynomial of an algebraic monoid, we introduce and study a $t$-analog of $q$-Stirling numbers.<\/jats:p>","DOI":"10.37236\/7986","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:08:26Z","timestamp":1578640106000},"source":"Crossref","is-referenced-by-count":1,"title":["A Geometric Interpretation of the Intertwining Number"],"prefix":"10.37236","volume":"26","author":[{"given":"Mahir Bilen","family":"Can","sequence":"first","affiliation":[]},{"given":"Yonah","family":"Cherniavsky","sequence":"additional","affiliation":[]},{"given":"Martin","family":"Rubey","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,4,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p7\/7820","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p7\/7820","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:15:04Z","timestamp":1579234504000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i2p7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,19]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,4,5]]}},"URL":"https:\/\/doi.org\/10.37236\/7986","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,4,19]]},"article-number":"P2.7"}}