{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:58:26Z","timestamp":1760061506481,"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>The set of $n$ by $n$ upper-triangular nilpotent matrices with entries in a finite field $\\mathbb{F}_q$ has Jordan canonical forms indexed by partitions $\\lambda \\vdash n$. We present a combinatorial formula for computing the number $F_\\lambda(q)$ of matrices of Jordan type $\\lambda$ as a weighted sum over standard Young tableaux. We construct a bijection between paths in a modified version of Young's lattice and non-attacking rook placements, which leads to a refinement of the formula for $F_\\lambda(q)$.<\/jats:p>","DOI":"10.37236\/6888","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:35:43Z","timestamp":1578670543000},"source":"Crossref","is-referenced-by-count":1,"title":["Rook Placements and Jordan Forms of Upper-Triangular Nilpotent Matrices"],"prefix":"10.37236","volume":"25","author":[{"given":"Martha","family":"Yip","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,3,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p68\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p68\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:37:06Z","timestamp":1579235826000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p68"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/6888","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,3,29]]},"article-number":"P1.68"}}