Proofs of two conjectures on Catalan triangle numbers
| Autor: | Xiuguo Lian, Victor J. W. Guo |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Algebra and Number Theory
Mathematics - Number Theory Applied Mathematics 05A30 05A10 11B65 010102 general mathematics 0102 computer and information sciences Mathematical proof 01 natural sciences language.human_language Combinatorics Catalan number 010201 computation theory & mathematics FOS: Mathematics language Mathematics - Combinatorics Catalan Combinatorics (math.CO) Number Theory (math.NT) 0101 mathematics Cyclotomic polynomial Analysis Mathematics |
| Zdroj: | Journal of Difference Equations and Applications. 24:1473-1487 |
| ISSN: | 1563-5120 1023-6198 |
| DOI: | 10.1080/10236198.2018.1501041 |
| Popis: | We prove two conjectures on sums of products of Catalan triangle numbers, which were originally conjectured by Miana, Ohtsuka, and Romero [Discrete Math. 340 (2017), 2388--2397]. The first one is proved by using Zeilberger's algorithm, and the second one is proved by establishing its $q$-analogue. Comment: 15 pages, to appear in J. Difference Equ. Appl |
| Databáze: | OpenAIRE |
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