On the total number of ones associated with cranks of partitions modulo 11
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909381969313792 |
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| author | Chen, Dandan Chen, Rong Yin, Siyu |
| author_facet | Chen, Dandan Chen, Rong Yin, Siyu |
| contents | In 2021, Andrews mentioned that George Beck introduced partition statistics $M_w(r,m,n)$, which denote the total number of ones in the partition of $n$ with crank congruent to $r$ modulo $m$. Recently, a number of congruences and identities involving $M_w(r,m,n)$ for some small $m$ have been developed. We establish the 11-dissection of the generating functions for $M_ω(r,11,n)-M_ω(11-r,11,n)$, where $r=1,2,3,4,5$. In particular, we discover a beautiful identity involving $M_ω(r,11,11n+6)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08450 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the total number of ones associated with cranks of partitions modulo 11 Chen, Dandan Chen, Rong Yin, Siyu Combinatorics Number Theory In 2021, Andrews mentioned that George Beck introduced partition statistics $M_w(r,m,n)$, which denote the total number of ones in the partition of $n$ with crank congruent to $r$ modulo $m$. Recently, a number of congruences and identities involving $M_w(r,m,n)$ for some small $m$ have been developed. We establish the 11-dissection of the generating functions for $M_ω(r,11,n)-M_ω(11-r,11,n)$, where $r=1,2,3,4,5$. In particular, we discover a beautiful identity involving $M_ω(r,11,11n+6)$. |
| title | On the total number of ones associated with cranks of partitions modulo 11 |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2410.08450 |