{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T19:41:06Z","timestamp":1773776466655,"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>Rook numbers of complementary boards are related by a reciprocity law. A complicated formula for this law has been known for about fifty years, but recently Gessel and the present author independently obtained a much more elegant formula, as a corollary of more general reciprocity theorems. Here, following a suggestion of Goldman, we provide a direct combinatorial proof of this new formula.<\/jats:p>","DOI":"10.37236\/1234","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:50:18Z","timestamp":1578707418000},"source":"Crossref","is-referenced-by-count":6,"title":["A Short Proof of the Rook Reciprocity Theorem"],"prefix":"10.37236","volume":"3","author":[{"given":"Timothy","family":"Chow","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1996,3,4]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i1r10\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i1r10\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T06:17:46Z","timestamp":1579328266000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v3i1r10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,3,4]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1996,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1234","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,3,4]]},"article-number":"R10"}}