{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:55Z","timestamp":1753893835593,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We present a bijective proof of Shapiro's convolution formula involving Catalan numbers of even index. As a corollary, we give a new interpretation of the Catalan numbers.<\/jats:p>","DOI":"10.37236\/3909","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:04:14Z","timestamp":1578704654000},"source":"Crossref","is-referenced-by-count":0,"title":["A Bijective Proof of Shapiro's Catalan Convolution"],"prefix":"10.37236","volume":"21","author":[{"given":"P\u00e9ter","family":"Hajnal","sequence":"first","affiliation":[]},{"given":"G\u00e1bor V.","family":"Nagy","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2014,5,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i2p42\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i2p42\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:58:54Z","timestamp":1579258734000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i2p42"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5,28]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2014,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/3909","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,5,28]]},"article-number":"P2.42"}}