An Alternative Generating Function for $k$-Regular Partitions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866929729056014336 |
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| author | Kurşungöz, Kağan |
| author_facet | Kurşungöz, Kağan |
| contents | We construct a $k$-fold $q$-series as a generating function of $k$-regular partitions for each positive integer $k$. The $k=1$ case is one of Euler's $q$-series identities pertaining to the partitions into distinct parts. The construction is combinatorial. Although we find a connection to Bessel polynomials in the $k=2$ case, this note is certainly not a study of Bessel polynomials and their $q$-analogs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17117 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Alternative Generating Function for $k$-Regular Partitions Kurşungöz, Kağan Combinatorics 05A17, 05A15, 11P84 We construct a $k$-fold $q$-series as a generating function of $k$-regular partitions for each positive integer $k$. The $k=1$ case is one of Euler's $q$-series identities pertaining to the partitions into distinct parts. The construction is combinatorial. Although we find a connection to Bessel polynomials in the $k=2$ case, this note is certainly not a study of Bessel polynomials and their $q$-analogs. |
| title | An Alternative Generating Function for $k$-Regular Partitions |
| topic | Combinatorics 05A17, 05A15, 11P84 |
| url | https://arxiv.org/abs/2502.17117 |