{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T13:15:53Z","timestamp":1773321353220,"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>Hankel matrices consisting of Catalan numbers have been analyzed by various authors. Desainte-Catherine and Viennot found their determinant to be $\\prod_{1 \\leq i \\leq j \\leq k} {{i+j+2n}\\over {i+j}}$ and related them to the Bender - Knuth conjecture. The similar determinant formula $\\prod_{1 \\leq i \\leq j \\leq k} {{i+j-1+2n}\\over {i+j-1}}$ can be shown to hold for Hankel matrices whose entries are successive middle binomial coefficients ${{2m+1} \\choose m}$. Generalizing the Catalan numbers in a different direction, it can be shown that determinants of Hankel matrices consisting of numbers ${{1}\\over {3m+1}} {{3m+1} \\choose m}$ yield an alternate expression of two Mills \u2013  Robbins \u2013 Rumsey determinants important in the enumeration of plane partitions and alternating sign matrices. Hankel matrices with determinant 1 were studied by Aigner in the definition of Catalan \u2013 like numbers. The well - known relation of Hankel matrices to orthogonal polynomials further yields a combinatorial application of the famous Berlekamp \u2013 Massey algorithm in Coding Theory, which can be applied in order to calculate the coefficients in the three \u2013 term recurrence of the family of orthogonal polynomials related to the sequence of Hankel matrices.<\/jats:p>","DOI":"10.37236\/1595","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:07:32Z","timestamp":1578708452000},"source":"Crossref","is-referenced-by-count":26,"title":["Some Aspects of Hankel Matrices in Coding Theory and Combinatorics"],"prefix":"10.37236","volume":"8","author":[{"given":"Ulrich","family":"Tamm","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2001,5,26]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1a1\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1a1\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:18:02Z","timestamp":1579324682000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i1a1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,5,26]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2001,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1595","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,5,26]]},"article-number":"A1"}}