A polynomial bosonic form of statistical configuration sums and the odd/even minimal excludant in integer partitions
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908828150267904 |
|---|---|
| author | Takagi, Taichiro |
| author_facet | Takagi, Taichiro |
| contents | Inspired by the study of the minimal excludant in integer partitions by G.E. Andrews and D. Newman, we introduce a pair of new partition statistics, sqrank and rerank. They are related to a polynomial bosonic form of statistical configuration sums for an integrable cellular automaton. For all nonnegative integers $n$, we prove that the partitions of $n$ on which sqrank or rerank takes on a particular value, say $r$, are equinumerous with the partitions of $n$ on which the odd/even minimal exclutant takes on the corresponding value, $2r+1$ or $2r+2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A polynomial bosonic form of statistical configuration sums and the odd/even minimal excludant in integer partitions Takagi, Taichiro Combinatorics 05A17, 05A30, 11P83, 05E10, 82B23 Inspired by the study of the minimal excludant in integer partitions by G.E. Andrews and D. Newman, we introduce a pair of new partition statistics, sqrank and rerank. They are related to a polynomial bosonic form of statistical configuration sums for an integrable cellular automaton. For all nonnegative integers $n$, we prove that the partitions of $n$ on which sqrank or rerank takes on a particular value, say $r$, are equinumerous with the partitions of $n$ on which the odd/even minimal exclutant takes on the corresponding value, $2r+1$ or $2r+2$. |
| title | A polynomial bosonic form of statistical configuration sums and the odd/even minimal excludant in integer partitions |
| topic | Combinatorics 05A17, 05A30, 11P83, 05E10, 82B23 |
| url | https://arxiv.org/abs/2412.19503 |