Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.07261 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929566476402688 |
|---|---|
| author | Deilami, Mehdi Nikopour Zhelyabovskyy, Bohdan |
| author_facet | Deilami, Mehdi Nikopour Zhelyabovskyy, Bohdan |
| contents | $n$-circuits are series-parallel networks composed of exactly $n$ unit resistors. This paper is focused on evaluating the mean resistance of all $n$-circuits, $M_n$, establishing that it lies between $1$ and $4.3954$ for all $n$. We ultimately conjecture that $M_n$ converges to $1.25$ as $n$ grows, based on computational analysis and other intuitive arguments. Although the number of $n$-circuits has been explored quite thoroughly, this paper also provides complete proofs of some important results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07261 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Average Resistance of n-circuits Deilami, Mehdi Nikopour Zhelyabovskyy, Bohdan Combinatorics Strongly Correlated Electrons 05A99 (Primary), 94C99 (Secondary) $n$-circuits are series-parallel networks composed of exactly $n$ unit resistors. This paper is focused on evaluating the mean resistance of all $n$-circuits, $M_n$, establishing that it lies between $1$ and $4.3954$ for all $n$. We ultimately conjecture that $M_n$ converges to $1.25$ as $n$ grows, based on computational analysis and other intuitive arguments. Although the number of $n$-circuits has been explored quite thoroughly, this paper also provides complete proofs of some important results. |
| title | On the Average Resistance of n-circuits |
| topic | Combinatorics Strongly Correlated Electrons 05A99 (Primary), 94C99 (Secondary) |
| url | https://arxiv.org/abs/2410.07261 |