Distributions of parity differences and biases in partitions into distinct parts
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913773420281856 |
|---|---|
| author | Man, Siu Hang |
| author_facet | Man, Siu Hang |
| contents | For a partition $λ\vdash n$, we let $\operatorname{pd}(λ)$, the parity difference of $λ$, be the number of odd parts of $λ$ minus the number of even parts of $λ$. We prove for $c_0\in\mathbb{R}$ an asymptotic expansion for the number of partitions of $n$ into distinct parts with normalised parity difference $n^{- 1/4}\operatorname{pd}(λ)$ greater than $c_0$ as $n\to \infty$. As a corollary, we find the distribution of the parity differences and parity biases for partitions of $n$ into distinct parts. We also establish analogous results for generalised parity differences modulo $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_11909 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Distributions of parity differences and biases in partitions into distinct parts Man, Siu Hang Number Theory Combinatorics For a partition $λ\vdash n$, we let $\operatorname{pd}(λ)$, the parity difference of $λ$, be the number of odd parts of $λ$ minus the number of even parts of $λ$. We prove for $c_0\in\mathbb{R}$ an asymptotic expansion for the number of partitions of $n$ into distinct parts with normalised parity difference $n^{- 1/4}\operatorname{pd}(λ)$ greater than $c_0$ as $n\to \infty$. As a corollary, we find the distribution of the parity differences and parity biases for partitions of $n$ into distinct parts. We also establish analogous results for generalised parity differences modulo $N$. |
| title | Distributions of parity differences and biases in partitions into distinct parts |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2306.11909 |