{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T09:56:06Z","timestamp":1773395766001,"version":"3.50.1"},"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>For every finite graded poset $P$ with $\\hat{0}$ and $\\hat{1}$ we associate a certain formal power series $F_P(x) = F_P(x_1,x_2,\\dots)$ which encodes the flag $f$-vector (or flag $h$-vector) of $P$. A relative version $F_{P\/\\Gamma}$ is also defined, where $\\Gamma$ is a subcomplex of the order complex of $P$. We are interested in the situation where $F_P$ or $F_{P\/\\Gamma}$ is a symmetric function of $x_1,x_2,\\dots$. When $F_P$ or $F_{P\/\\Gamma}$ is symmetric we consider its expansion in terms of various symmetric function bases, especially the Schur functions. For a class of lattices called $q$-primary lattices the Schur function coefficients are just values of Kostka polynomials at the prime power $q$, thus giving in effect a simple new definition of Kostka polynomials in terms of symmetric functions. We extend the theory of lexicographically shellable posets to the relative case in order to show that some examples $(P,\\Gamma)$ are relative Cohen-Macaulay complexes. Some connections with the representation theory of the symmetric group and its Hecke algebra are also discussed.<\/jats:p>","DOI":"10.37236\/1264","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:52:12Z","timestamp":1578707532000},"source":"Crossref","is-referenced-by-count":9,"title":["Flag-symmetric and Locally Rank-symmetric Partially Ordered Sets"],"prefix":"10.37236","volume":"3","author":[{"given":"Richard P.","family":"Stanley","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1995,5,26]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i2r6\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i2r6\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T09:31:57Z","timestamp":1579339917000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v3i2r6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,5,26]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[1996,1,24]]}},"URL":"https:\/\/doi.org\/10.37236\/1264","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,5,26]]},"article-number":"R6"}}