Bibliographic Details
| Title: |
Euler-type recurrences for $t$-color and $t$-regular partition functions |
| Authors: |
Bhowmik, Tapas, Tsai, Wei-Lun, Ye, Dongxi |
| Publication Year: |
2024 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Number Theory, Mathematics - Combinatorics, 05A17, 11F11, 11F25, 11P81 |
| More Details: |
We give Euler-like recursive formulas for the $t$-colored partition function when $t=2$ or $t=3,$ as well as for all $t$-regular partition functions. In particular, we derive an infinite family of ``triangular number" recurrences for the $3$-colored partition function. Our proofs are inspired by the recent work of Gomez, Ono, Saad, and Singh on the ordinary partition function and make extensive use of $q$-series identities for $(q;q)_{\infty}$ and $(q;q)_{\infty}^3.$
Comment: 12 pages, 2 tables, corrected a typo in Theorem 1.1, added a new reference |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2412.14344 |
| Accession Number: |
edsarx.2412.14344 |
| Database: |
arXiv |
