{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T12:00:47Z","timestamp":1773144047949,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>An $r$-dual tower of groups is a nested sequence of finite groups, like the symmetric groups, whose Bratteli diagram forms an $r$-dual graded graph.\u00a0 Miller and Reiner introduced a special case of these towers in order to study the Smith forms of the up and down maps in a differential poset.\u00a0 Agarwal and the author have also used these towers to compute critical groups of representations of groups appearing in the tower.\u00a0 In this paper I prove that when $r=1$ or $r$ is prime, wreath products of a fixed group with the symmetric groups are the only $r$-dual tower of groups, and conjecture that this is the case for general values of $r$.\u00a0 This implies that these wreath products are the only groups for which one can define an analog of the Robinson-Schensted bijection in terms of a growth rule in a dual graded graph.<\/jats:p>","DOI":"10.37236\/7790","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:15:31Z","timestamp":1578640531000},"source":"Crossref","is-referenced-by-count":3,"title":["Dual Graded Graphs and Bratteli Diagrams of Towers of Groups"],"prefix":"10.37236","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3748-4008","authenticated-orcid":false,"given":"Christian","family":"Gaetz","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,2,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p25\/7784","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p25\/7784","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:18:03Z","timestamp":1579234683000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i1p25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/7790","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,22]]},"article-number":"P1.25"}}