{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:21Z","timestamp":1753893801761,"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>We give a basis for the space spanned by the sum $\\hat{s}_\\lambda$ of the lowest degree terms in the expansion of the Schur symmetric functions $s_\\lambda$ in terms of the power sum symmetric functions $p_\\mu$, where deg$(p_i)=1$. These lowest degree terms  correspond to minimal border strip tableaux of $\\lambda$.  The dimension of the space spanned by $\\hat{s}_\\lambda$, where $\\lambda$ is a partition of $n$, is equal to the number of partitions of $n$ into parts differing by at least 2. Applying     the Rogers-Ramanujan identity, the generating function also counts the number of partitions of $n$ into parts $5k+1$ and $5k-1$. We also show that a symmetric function closely related to $\\hat{s}_\\lambda$ has the same coefficients when expanded in terms of power sums or augmented monomial symmetric functions. <\/jats:p>","DOI":"10.37236\/1820","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:31:52Z","timestamp":1578709912000},"source":"Crossref","is-referenced-by-count":1,"title":["Bottom Schur Functions"],"prefix":"10.37236","volume":"11","author":[{"given":"Peter","family":"Clifford","sequence":"first","affiliation":[]},{"given":"Richard P.","family":"Stanley","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,9,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r67\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r67\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:53:44Z","timestamp":1579323224000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r67"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,9,24]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1820","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2004,9,24]]},"article-number":"R67"}}