A proof of some conjectures of Mao on partition rank inequalities
| Autor: | Elena Iannuzzi, Holly Swisher, Ethan Alwaise |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Algebra and Number Theory
Mathematics - Number Theory Inequality Mathematics::Number Theory Modulo media_common.quotation_subject 010102 general mathematics 01 natural sciences 010101 applied mathematics Combinatorics Number theory FOS: Mathematics Partition (number theory) Number Theory (math.NT) 11P83 0101 mathematics Mathematics media_common |
| Zdroj: | The Ramanujan Journal. 43:633-648 |
| ISSN: | 1572-9303 1382-4090 |
| DOI: | 10.1007/s11139-016-9789-x |
| Popis: | Based on work of Atkin and Swinnerton-Dyer on partition rank difference functions, and more recent work of Lovejoy and Osburn, Mao has proved several inequalities between partition ranks modulo $10$, and additional results modulo $6$ and $10$ for the $M_2$ rank of partitions without repeated odd parts. Mao conjectured some additional inequalities. We prove some of Mao's rank inequality conjectures for both the rank and the $M_2$ rank modulo $10$ using elementary methods. 12 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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