{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T02:34:36Z","timestamp":1772505276359,"version":"3.50.1"},"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 characterization of permutation polynomials over a finite field based on their coefficients, similar to Hermite's Criterion. Then, we use this result to obtain a formula for the total number of monic permutation binomials of degree less than $4p$ over ${\\Bbb F}_{4p+1}$, where $p$ and $4p+1$ are primes, in terms of the numbers of three special types of permutation binomials. We also briefly discuss the case $q=2p+1$ with $p$ and $q$ primes.<\/jats:p>","DOI":"10.37236\/1091","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:59:18Z","timestamp":1578718758000},"source":"Crossref","is-referenced-by-count":6,"title":["The Number of Permutation Binomials over ${\\Bbb F}_{4p+1}$ where $p$ and $4p+1$ are Primes"],"prefix":"10.37236","volume":"13","author":[{"given":"A.","family":"Masuda","sequence":"first","affiliation":[]},{"given":"D.","family":"Panario","sequence":"additional","affiliation":[]},{"given":"Q.","family":"Wang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,8,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r65\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r65\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:10:07Z","timestamp":1579320607000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r65"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,8,3]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1091","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,8,3]]},"article-number":"R65"}}