{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:58Z","timestamp":1753893838453,"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>We prove that for arbitrary partitions $\\mathbf{\\lambda} \\subseteq \\mathbf{\\kappa},$ and integers $0\\leq c&lt;r\\leq n,$ the sequence of Schur polynomials\u00a0$S_{(\\mathbf{\\kappa} + k\\cdot\\mathbf{1}^c)\/(\\mathbf{\\lambda} + k\\cdot\\mathbf{1}^r)}(x_1,\\dots,x_n)$ for $k$ sufficiently large,\u00a0satisfy a linear recurrence. The roots of the characteristic equation are given explicitly.\u00a0These recurrences are also valid for certain sequences of minors of banded Toeplitz matrices.In addition, we show that Widom's determinant formula from 1958 is a special case of a well-known identity for Schur polynomials.<\/jats:p>","DOI":"10.37236\/2651","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:11:37Z","timestamp":1578712297000},"source":"Crossref","is-referenced-by-count":8,"title":["Schur Polynomials, Banded Toeplitz Matrices and Widom's Formula"],"prefix":"10.37236","volume":"19","author":[{"given":"Per","family":"Alexandersson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2012,11,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p22\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p22\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:23:04Z","timestamp":1579299784000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i4p22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11,8]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2012,10,18]]}},"URL":"https:\/\/doi.org\/10.37236\/2651","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,11,8]]},"article-number":"P22"}}