Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2506.20296 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914307025928192 |
|---|---|
| author | Wang, Xu Zhu, Jiayi |
| author_facet | Wang, Xu Zhu, Jiayi |
| contents | The base sequences BS(n+1,n) are four sequences of $\pm1$ and lengths n+1,n+1,n,n with zero auto correlation. The base sequence conjecture states that BS(n+1,n) exists for all positive integers and has been verified for $n\le40$. We present our algorithm and give construction of BS(n+1,n) for $n=41,42,43$.\\ The Normal sequences NS (n) and the Near-normal sequences NNS (n) are subclasses of BS(n+1,n). Yang conjecture asserts that there is a NNS(n) for each even integer n and has been verified for $n\le40$. We found that there is no NNS(n) for n=42 and 44 by exhaustive search, which gives the first counter case of Yang conjecture. We also show that there is no NS(n) for n=41,42,43,44,45 by exhaustive search and proves that no NS(n) exist for $n=8k-2,k \in Z_+$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Base, Normal and Near-normal Sequences Wang, Xu Zhu, Jiayi Combinatorics The base sequences BS(n+1,n) are four sequences of $\pm1$ and lengths n+1,n+1,n,n with zero auto correlation. The base sequence conjecture states that BS(n+1,n) exists for all positive integers and has been verified for $n\le40$. We present our algorithm and give construction of BS(n+1,n) for $n=41,42,43$.\\ The Normal sequences NS (n) and the Near-normal sequences NNS (n) are subclasses of BS(n+1,n). Yang conjecture asserts that there is a NNS(n) for each even integer n and has been verified for $n\le40$. We found that there is no NNS(n) for n=42 and 44 by exhaustive search, which gives the first counter case of Yang conjecture. We also show that there is no NS(n) for n=41,42,43,44,45 by exhaustive search and proves that no NS(n) exist for $n=8k-2,k \in Z_+$. |
| title | On Base, Normal and Near-normal Sequences |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.20296 |