An inequality between finite analogues of rank and crank moments
| Autor: | Pramod Eyyunni, Bibekananda Maji, Garima Sood |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Crank
Algebra and Number Theory Mathematics - Number Theory Inequality media_common.quotation_subject Nuclear Theory 010102 general mathematics 11P80 11P81 11P82 05A17 0102 computer and information sciences 01 natural sciences Combinatorics 010201 computation theory & mathematics FOS: Mathematics Rank (graph theory) Number Theory (math.NT) 0101 mathematics Mathematics media_common |
| Zdroj: | International Journal of Number Theory. 17:405-423 |
| ISSN: | 1793-7310 1793-0421 |
| DOI: | 10.1142/s1793042120400217 |
| Popis: | The inequality between rank and crank moments was conjectured and later proved by Garvan himself in 2011. Recently, Dixit and the authors introduced finite analogues of rank and crank moments for vector partitions while deriving a finite analogue of Andrews’ famous identity for smallest parts function. In the same paper, they also conjectured an inequality between finite analogues of rank and crank moments, analogous to Garvan’s conjecture. In this paper, we give a proof of this conjecture. |
| Databáze: | OpenAIRE |
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