Fractional partitions and conjectures of Chern–Fu–Tang and Heim–Neuhauser
| Autor: | Zack Tripp, Kathrin Bringmann, Larry Rolen, Ben Kane |
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| Rok vydání: | 2021 |
| Předmět: |
Discrete mathematics
Conjecture 010102 general mathematics Multiplicative function Context (language use) 0102 computer and information sciences General Medicine Partition function (mathematics) 01 natural sciences Range (mathematics) Future study 010201 computation theory & mathematics Partition (number theory) 0101 mathematics Mathematics |
| Zdroj: | Transactions of the American Mathematical Society, Series B. 8:615-634 |
| ISSN: | 2330-0000 |
| DOI: | 10.1090/btran/77 |
| Popis: | Many papers have studied inequalities for partition functions. Recently, a number of papers have considered mixtures between additive and multiplicative behavior in such inequalities. In particular, Chern–Fu–Tang and Heim–Neuhauser gave conjectures on inequalities for coefficients of powers of the generating partition function. These conjectures were posed in the context of colored partitions and the Nekrasov–Okounkov formula. Here, we study the precise size of differences of products of two such coefficients. This allows us to prove the Chern–Fu–Tang conjecture and to show the Heim–Neuhauser conjecture in a certain range. The explicit error terms provided will also be useful in the future study of partition inequalities. These are laid out in a user-friendly way for the researcher in combinatorics interested in such analytic questions. |
| Databáze: | OpenAIRE |
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