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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2001.00162 |
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| _version_ | 1866916133842452480 |
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| author | He, Thomas Y. Ji, Kathy Q. Zhao, Alice X. H. |
| author_facet | He, Thomas Y. Ji, Kathy Q. Zhao, Alice X. H. |
| contents | The main objective of this paper is to present an answer to Bressoud's conjecture for the case $j=0$, resulting in a complete solution to the conjecture. The case for $j=1$ has been recently resolved by Kim. Using the connection established in our previous paper between the ordinary partition function $B_0$ and the overpartition function $\overline{B}_1$, we found that the proof of Bressoud's conjecture for the case $j=0$ is equivalent to establishing an overpartition analogue of the conjecture for $j=1$. By generalizing Kim's method, we obtain the desired overpartition analogue of Bressoud's conjecture for $j=1$, which eventually enables us to confirm Bressoud's conjecture for the case $j=0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_00162 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Overpartitions and Bressoud's conjecture, II He, Thomas Y. Ji, Kathy Q. Zhao, Alice X. H. Combinatorics 05A17, 05A30, 11P84, 11P81, 33A65 The main objective of this paper is to present an answer to Bressoud's conjecture for the case $j=0$, resulting in a complete solution to the conjecture. The case for $j=1$ has been recently resolved by Kim. Using the connection established in our previous paper between the ordinary partition function $B_0$ and the overpartition function $\overline{B}_1$, we found that the proof of Bressoud's conjecture for the case $j=0$ is equivalent to establishing an overpartition analogue of the conjecture for $j=1$. By generalizing Kim's method, we obtain the desired overpartition analogue of Bressoud's conjecture for $j=1$, which eventually enables us to confirm Bressoud's conjecture for the case $j=0$. |
| title | Overpartitions and Bressoud's conjecture, II |
| topic | Combinatorics 05A17, 05A30, 11P84, 11P81, 33A65 |
| url | https://arxiv.org/abs/2001.00162 |