| Автор | Paule, Peter |
| Дата выпуска | 1996 |
| dc.description | From numerical experiments, D. E. Knuth conjectured that 0 < D <sub>n+4</sub> < D <sub>n</sub> for a combinatorial sequence (D<sub>n</sub> ) defined as the difference D<sub>n</sub> = R<sub>n</sub> – L<sub>n</sub> of two definite hypergeometric sums. The conjecture implies.an identity of type L<sub>n</sub> = |R<sub>n</sub> |, involving the floor function. We prove Knuth's conjecture by applying Zeilberger's algorithm as well as classical hypergeometric machinery. |
| Формат | application.pdf |
| Издатель | Taylor & Francis Group |
| Копирайт | Copyright Taylor and Francis Group, LLC |
| Название | A Proof of a Conjecture of Knuth |
| Тип | research-article |
| DOI | 10.1080/10586458.1996.10504579 |
| Electronic ISSN | 1944-950X |
| Print ISSN | 1058-6458 |
| Журнал | Experimental Mathematics |
| Том | 5 |
| Первая страница | 83 |
| Последняя страница | 89 |
| Аффилиация | Paule, Peter; Institut für Mathematik, RISC, J. Kepler Universitat Linz |
| Выпуск | 2 |
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| Библиографическая ссылка | Paule, P. and Schorn, M. “A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities” [Paule and Schorn 1995], RISC-Linz, Report Series 95–10; to appear in J. Symb. Comput. (special issue on “Symbolic Computation in Combinatorics dgr;1”, edited by P. Paule and V. Strehl). The softare is available at ftp://ftp.risc.unilinz.ac.at/pub/combinatorics/mathematica/PauleSchorn |
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