Locally Semi-Equitable Colourings of BIBDs
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910236701360128 |
|---|---|
| author | Burgess, Andrea C. Kellough, William Pike, David A. |
| author_facet | Burgess, Andrea C. Kellough, William Pike, David A. |
| contents | We study $\ell$-colourings of $(v,k,λ)$-BIBDs (balanced incomplete block designs) where, within each block, one colour is absent and each of the $\ell-1$ other colours appears exactly $\frac{k}{\ell-1}$ times. We establish several necessary conditions for such colourings to exist. We also use these coloured BIBDs to provide new necessary conditions for the existence of Hadamard matrices, affine planes, and twin prime powers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20002 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Locally Semi-Equitable Colourings of BIBDs Burgess, Andrea C. Kellough, William Pike, David A. Combinatorics 05B05, 05C15 We study $\ell$-colourings of $(v,k,λ)$-BIBDs (balanced incomplete block designs) where, within each block, one colour is absent and each of the $\ell-1$ other colours appears exactly $\frac{k}{\ell-1}$ times. We establish several necessary conditions for such colourings to exist. We also use these coloured BIBDs to provide new necessary conditions for the existence of Hadamard matrices, affine planes, and twin prime powers. |
| title | Locally Semi-Equitable Colourings of BIBDs |
| topic | Combinatorics 05B05, 05C15 |
| url | https://arxiv.org/abs/2605.20002 |