{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:17Z","timestamp":1753893857049,"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>Let $V$ be an infinite matrix with rows and columns indexed by the positive integers, and entries in a field $F$. Suppose that $v_{i,j}$ only depends on $i-j$ and is 0 for $|i-j|$ large. Then $V^{n}$ is defined for all $n$, and one has a \"generating function\" $G=\\sum a_{1,1}(V^{n})z^{n}$. Ira Gessel has shown that $G$ is algebraic over $F(z)$. We extend his result, allowing $v_{i,j}$ for fixed $i-j$ to be eventually periodic in $i$ rather than constant. This result and some variants of it that we prove will have applications to Hilbert-Kunz theory.<\/jats:p>","DOI":"10.37236\/492","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:57:31Z","timestamp":1578715051000},"source":"Crossref","is-referenced-by-count":0,"title":["Generating Functions Attached to some Infinite Matrices"],"prefix":"10.37236","volume":"18","author":[{"given":"Paul","family":"Monsky","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,1,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:18:25Z","timestamp":1579303105000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/492","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,1,5]]},"article-number":"P5"}}