{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T16:42:06Z","timestamp":1759941726410,"version":"3.41.2"},"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>This paper explores the orbit structure and homomesy (constant averages over orbits)\u00a0properties of certain actions of toggle groups on the collection of independent sets of a\u00a0path graph. In particular we prove a generalization of a homomesy conjecture of Propp\u00a0that for the action of a \"Coxeter element\" of vertex toggles,\u00a0the difference of indicator functions of symmetrically-located vertices is 0-mesic.\u00a0Then we use our analysis to show facts about orbit sizes that are easy to conjecture but\u00a0nontrivial to prove.\u00a0Besides its intrinsic interest, this particular combinatorial dynamical system is valuable in\u00a0providing an interesting example of (a) homomesy in a context where large orbit sizes make a\u00a0cyclic sieving phenomenon unlikely to exist, (b) the use of Coxeter theory to greatly\u00a0generalize the set of actions for which results hold, and (c) the usefulness of Striker's\u00a0notion of generalized toggle groups.<\/jats:p>","DOI":"10.37236\/6755","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:41:31Z","timestamp":1578670891000},"source":"Crossref","is-referenced-by-count":2,"title":["Toggling Independent Sets of a Path Graph"],"prefix":"10.37236","volume":"25","author":[{"given":"Michael","family":"Joseph","sequence":"first","affiliation":[]},{"given":"Tom","family":"Roby","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,1,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p18\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p18\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:41:02Z","timestamp":1579236062000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/6755","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,1,25]]},"article-number":"P1.18"}}