{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:41Z","timestamp":1753893821766,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $\\lambda$ be a partition of a positive integer $n$. The genomic Schur function $U_\\lambda$ was introduced by Pechenik-Yong in the context of the $K$-theory of Grassmannians. Recently, Pechenik provided a positive combinatorial formula for the fundamental quasisymmetric expansion of $U_\\lambda$ in terms of increasing gapless tableaux. In this paper, for each $1 \\le m \\le n$, we construct an $H_m(0)$-module $\\mathbf{G}_{\\lambda;m}$ whose image under the quasisymmetric characteristic is the $m$th degree homogeneous component of $U_\\lambda$ by defining an $H_m(0)$-action on increasing gapless tableaux. We provide a method to assign a permutation to each increasing gapless tableau, and use this assignment to decompose $\\mathbf{G}_{\\lambda;m}$ into a direct sum of weak Bruhat interval modules. Furthermore, we determine the projective cover of each summand of the direct sum decomposition.<\/jats:p>","DOI":"10.37236\/12896","type":"journal-article","created":{"date-parts":[[2024,12,26]],"date-time":"2024-12-26T17:23:32Z","timestamp":1735233812000},"source":"Crossref","is-referenced-by-count":1,"title":["Weak Bruhat Interval Modules for Genomic Schur Functions"],"prefix":"10.37236","volume":"31","author":[{"given":"Young-Hun","family":"Kim","sequence":"first","affiliation":[]},{"given":"Semin","family":"Yoo","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2024,12,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i4p73\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i4p73\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,26]],"date-time":"2024-12-26T17:23:32Z","timestamp":1735233812000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i4p73"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,27]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,10,3]]}},"URL":"https:\/\/doi.org\/10.37236\/12896","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2024,12,27]]},"article-number":"P4.73"}}